President Reagan and his Democratic challenger, Walter F. Mondale, kick off their fall campaigns Monday with a shared belief that the outcome will shape the nation's future but with very different strategies for winning the race.

Holding the biggest pre-Labor Day polling advantage of any incumbent in 12 years -- but one his strategists say is not erosion-proof -- Reagan hopes to amass an electoral college victory as big as his 44-state sweep in 1980. That kind of landslide could power the Republican Party to gains all along the ballot and give Reagan a mandate for policy changes as profound as those of Franklin D. Roosevelt's "Second New Deal" after his second-term victory in 1936.

Mondale, by contrast, seeks to exploit the sharp divisions between voting blocs created by the "Reagan Revolution" of the past 44 months and hopes to trigger a huge increase in voter turnout. Even if that happens, aides concede that Mondale would be lucky to eke out a narrow electoral college victory. But that would be enough to arrest the Reagan Revolution in government and put the country on a significantly different path.

Trailing everywhere, Mondale wants to "come out smoking" and try for an across-the-board increase in his share of the vote. That desire is symbolized by Mondale's Labor Day sweep, accompanied by running mate Geraldine A. Ferraro, from New York City through Wisconsin to Long Beach, Calif. -- literally from sea to sea.

His goal, says campaign chairman James A. Johnson, is to "raise the stakes" for the voters by stressing his disagreements with Reagan policies that he claims will endanger America's future. To emphasize his drive, he will stump in the early part of the week with Rep. Ferraro (D-N.Y.), whose presence on the ticket has given it most of what zing it has exhibited this summer.

Reagan will "come out stroking," starting his campaign in friendly territory in his home state of California, while Vice President Bush spends the week mainly in the South. The West and the South offer the Republicans a seemingly secure electoral base -- something Mondale lacks.

A week later, Reagan will carry the attack to Mondale in the more marginal Midwest and Northeast. The president will start at a measured pace, according to campaign director Edward J. Rollins, then increase the pressure as Election Day nears. And though Republicans assume that Mondale will deliver what Rollins called "a pretty shrill attack" on Reagan's policies, "the president will not respond," but rather will emphasize his themes of strong leadership and continued economic growth, Rollins said.

The opening gambits are shaped by the contrasting political needs of the two campaigns. Reagan starts with a lead of 52 percent to 41 percent over Mondale in the August Gallup Poll, the best position for an incumbent president since Richard M. Nixon's 34-point lead over George McGovern in 1972.

But the history of polling bears out the warnings against complacency that filled the GOP convention hall in Dallas last month. Four years ago, President Jimmy Carter had a 6-point lead over challenger Reagan in August and lost by more than 9 points -- a 15-point swing. In 1976, a similar swing carried Republican President Gerald R. Ford up from a 17-point deficit to a narrow 2-point loss. In 1968, Hubert H. Humphrey started out 16 points behind Nixon and ended up losing by less than 1 point.

And, in the classic upset often cited by Reagan in a warning against overconfidence, President Harry S Truman trailed Thomas E. Dewey by 13 points in August 1948 and beat him by 4 points in November.

That is not the whole story, of course. In both 1952 and 1956, Republican Dwight D. Eisenhower started ahead and never let Adlai E. Stevenson get close. Democrat Lyndon B. Johnson kept Barry Goldwater pinned to the mat in 1964, as Nixon did McGovern in 1972.

Lawrence F. O'Brien, who worked for winner Johnson in 1964 and for loser Humphrey in 1968, said in a telephone interview that Mondale is better positioned for an upset than Humphrey -- Mondale's mentor -- was in 1968.

"We had the Vietnam issue which had alienated millions of Democrats," O'Brien said. "He has no such issue and no such defections. We had not campaigned in the primaries and had no organization on Labor Day. He has been through a tough campaign and has his organization in place.

"We were strapped for money and had a hard time raising it; we were constantly delaying and cutting back our TV ads. They have the federal financing and can go on the air when they want. We could not get Congress to grant the waiver for presidential debates. They are assured of at least one debate with Reagan. In every respect," O'Brien said, "Fritz Mondale is looking at a much better situation."

But Mondale is also running against a politician who has never lost a general election campaign, and running against the power of the White House, which Humphrey did not have to face.

Two elements in the politics of 1984 add to the uncertainty. Ferraro is the first woman on a major-party ticket, and has been drawing so much attention -- both favorable and unfavorable -- that Rollins suggested, not entirely tongue-in-cheek, that one of Mondale's main objectives in the next few weeks must be "to get himself out front and get her on the back pages, where vice-presidential candidates are supposed to live."

The second unknown is the outcome of the registration race in which both parties are now fully engaged. With help promised from Jesse L. Jackson, whose presidential nomination bid helped swell the ranks of black voters, Democrats hope to enfranchise millions more of the low-income voters likely to back their ticket.

Republicans claim that, so far, they have at least kept pace by targeting military families, young business people who have moved and, particularly, evangelical Christians, and adding more than 2 million of them to the rolls.

In trying to play Truman rather than McGovern, Mondale is targeting by demography, rather than geography -- a judgment the Republicans think is a mistake. Rollins and others have questioned why Mondale and Ferraro did not use August in an effort to "nail down their base," the band of states between his Minnesota and her New York, rather than scattershot their efforts through the South, the West Coast and the Great Plains.

The critics will raise more questions about this week's schedule, which shows Mondale and Ferraro heavily committed in California -- where Reagan has never been beaten -- and campaigning also in places like Spokane, Wash., and Merrill, Wis., which are hardly centers of Democratic strength.

But Johnson contends that the August effort paid dividends and asserts that "Mondale can make a similar case in any state and move the voter numbers nationally." To the extent that there is targeting now, he said, it is aimed at "Democrats who voted for Reagan in 1980 and both Democrats and independents who voted for Gary Hart in the 1984 primaries." (Colorado Sen. Hart was a Democratic presidential contender.)

Republicans agree that the target groups for 1984 are those 1980 blue-collar Democrats-for-Reagan and the "Yuppies," ticket-splitting Democrats and independents who liked Hart last spring. But they think they are wooing them better than Mondale is.

The logic of the Republicans' schedule is evident. Reagan opens in California and Utah to "solidify his base," as Rollins put it, then goes to Chicago for the first foray into the Midwest-Northeast area that ought to be Mondale-Ferraro territory but so far, the polls say, is not. Next week, he will concentrate on the Northeast. Bush, meantime, is working the South and the border states and then will swing into the Midwest.

By this technique, Rollins said, Republicans "can test if the leads we have in what should be their territory are solid. If they are -- if they hold up through Oct. 1 -- we can go for a big win, a 50-state strategy. If not, we still have a strong base on which to fall back."

Mondale's strategy is riskier, but the trailing candidate has fewer options. "No one is talking conservative tactics, when we're down 12 to 15 points," Johnson said. "We have to carry the challenge to Reagan, and establish from the outset that this is going to be a very aggressive campaign."

Wherever Mondale campaigns, Johnson said, his aim will be to show the voters "this is a critical election, whose outcome can affect their future and that of their children."

Mondale, according to senior adviser Richard C. Leone, will hit hardest on four related themes, contending that:

*His disagreement with Reagan on arms control and the nuclear weapons freeze could make the difference between a safer and a more dangerous world.

*His challenge to Reagan to raise taxes and curb the budget deficit could make the difference between a secure economic future and one dominated by growing government debt and the threat of imports.

*His opposition to Reagan's domestic-spending cuts could make the difference between a government oriented to average citizens and one devoted to the rich.

*His criticism of Reagan's stands on school prayer and anti-abortion amendments could make the difference between a policy of tolerance and one of conformity imposed on private conscience.

All these, of course, are Democratic formulations. Johnson and Leone said their polls showed that Mondale made "substantial progress" in establishing the deficit-tax issue in people's minds last month and that there is a receptive climate for the other three issues as well.

Republicans claim they have answers for all these questions, arguing for example that they can turn the tax issue against Mondale by drumming home the message that his budget plan would sock the average family with a $1,500-a-year tax hike, while Reagan will try for further rate reductions in his promised tax reform. On defense, domestic spending and the social issues, too, Republicans think they hold the high ground.

But Rollins made it plain that Reagan is likely, in this early phase of the game, to talk about the future in more generalized terms, emphasizing the contrast between today's strong economy and strong defense and the "stagflation" and "military weakness" he says he inherited from the Carter-Mondale administration.

He will also dwell heavily on the question of "leadership," where poll after poll show him far out in front of Mondale, and where Republicans contend the Democratic nominee has a fatal weakness. That opinion is not confined to the Republican ranks; when Democratic governors met with Mondale a week ago, they told him he had to "let his hair down" and show more of his natural personality in order to compete with Reagan.

Mondale responded to that suggestion only by saying he would "continue to tell the truth." Johnson, saying his long-time boss is "way beyond the stage where a makeup artist is going to retouch his coloring and hairline," declared that the only image-making planned for this month is to restore the reputation Mondale won among Democrats in the spring primaries, when he battled back from losses to Hart in New Hampshire and Maine to claim the nomination.

"The principal task," Johnson said, "is for him to be unmistakably again what he was in March -- sincerely standing up for what he believes, in a race he intends to win, showing toughness, tenacity and laying it on the line."

Television ads are scheduled to begin emerging soon from both camps, and by the third week in September, Rollins and Johnson both predicted, there could be a televised debate between Reagan and Mondale. Although the first negotiations on debates ended inconclusively Friday, the strategies of the two campaigns seem to be coinciding to produce such a confrontation this month.

Seeking to sharpen the issues and hype public interest before voter registration deadlines pass, the Democrats, according to Johnson, "want the first debate as early in September as we can get it."

Rollins, who expresses the White House confidence that "Reagan has never lost a debate," nonetheless wants all the debating finished by the first week in October, "so we can control the schedule and the content of the last month of the campaign to meet our political needs -- not someone else's."

Both sides agree that when the debate occurs the first phase of the campaign will be ended. What they don't know -- on either side -- is whether it will then look like a real horse race or a walkover.