Tuesday's showdown between John Ray and Douglas E. Moore for an atlarge seat on the D.C. City Council has emerged as a political war between two different Washingtons, each trying to establish itself as the dominant force in the District's developing home rule politics.

Moore expects most of his support to come from among blacks. They include the church elders and older women in Suhday's plumed and feathered hats; and the bulky-armed brick-layers and Metro tunnel workers finally able to buy homes of their own near Fort Dupont Park. There are professional community activists in Adams-Morgan and mail clerks in the row houses off South Capitol Street in Anacostia. There are the teachers in the roomy, comfortable homes around Catholic University and the bus drivers and blue-collar workers in their brick houses with green-and-white awnings off upper Georgia Avenue.

Ray's army contains many whites -- the middle-aged civic-minded liberals of Georgetown: the gays in the Victorian houses of DuPont Circle and town houses near Waterside mall: the neighborhood activists of Cleveland Park and the senior citizens in the high rises along Connecticut Avenue. There also are young black professionals in New Southwest and the black upper middle-class along the winding slopes off upper 16th Street NW.

Strategists agree that the election will be decided not necessarily on issues, but on which side will be best able to arouse its supporters and get them to the polls Tuesday.

"There is a certain sympathy and identity with a man who is identified as the leader of a struggle. There is a certain calling," said Moore strategist David Chatman. "Many people perceive Doug as a wounded person, a person who has been mistreated by the media and others. We have found a way to translate that sentiment into votes."

Ted Gay, Ray's campaign manager, sees it differently. "People feel this city is on the verge of new horizons and change is in the air. If we're going to accomplish anything, we need someone who is going to get things done," he said yesterday.

"We've concentrated our effort on reaching those who we feel are going to vote, and we've worked them in such a way that they're going to vote for John Ray," he said.

Even though it is a special election to fill the remaining 19 months of the term vacated by Marion Barry when he became mayor in January, Tuesday's contest carries high personal stakes for two of the city's most prominent politicians -- Moore and Barry.

Moore, the 50-year-old Methodist minister, former chairman of the activist Black United Front and once a highly popular member of the City Council, is trying to make a political comeback. In last year's battle for the Democratic nomination for City Council chairman, Moore's brand of doctrinaire confrontation politics and personal conduct was soundly rejected. If his "new image" campaign fails in this election, Moore's political future could become uncertain.

Ray, a 35-year-old lawyer and new-comer to city politics who was appointed to the seat until the election, has only his own infant political career at risk. But Mayor Barry has actively endorsed Ray and put many of his scrappy political irregulars to work on Ray's behalf. This is the first real test of Barry's political power as mayor, and, some observers believe, an early loss could be significant.

Tuesday will mark the second time the city has had a special election for a City Council at-large seat. On July 19, 1977. Hilda Mason beat former D.C. School Superintendent Barbara A. Sizemore by an 18-1 margin in the high-turnout area of the city west of Rock Creek Park to clinch victory in a close contest.

Mason, Sizemore and eight others were competing to fill the at-large vacancy created by the March 23 death of Julius W. Hobson Sr. In the 1977 election, some 25000 persons voted.

There are eleven candidates in Tuesday's at-large Council contest, Moore and Ray are the generally acknowledged front runners. Strategists for both sides expect about 50,000 of the city's 250,750 registered voters to go to the polls. They expect more people to vote on Tuesday than in 1977 because interest in the election may have been heightened by two other contests on the ballot.

Fifteen candidates are campaigning to replace Council Chairman Arrington Dixon as the Ward 4 representative on the council. There are 10 others in the field of candidates to fill the at-large vacancy created on the school board when Betty Ann Kane was elected to the City Council last year. The at-large council race has attracted the most attention and heaviest financial contributions.

Strategists for Moore and Ray already have divided up the city and staked out largely uncontested political bases where their respective candidates are expected to run best.

For Moore, that area is in the largely black and lower-to-middle-income far northeast and southeast sections of the city.

It is in these areas -- wards 5, 7 and 8 -- where, according to Moore strategists. Moore ran best in his successful Council race in 1974, and in his unsuccessful council chairman race in 1978. They also are areas to where Size-more, whose political strategy Moore helped to fashion, did best in 1977.

"Doug Moore has a base. We are going to build on that base," Chatman said.

Ray has worked in these areas and hopes to do well. But, conceded Ray campaign manager Gay, they are areas where Moore is strong. "We may end up carrying them," Gay said last week. "We may not, But one thing is for sure -- we won't get clobbered in them."

Both sides expect between 26,000 to 27,000 votes will be necessary to win -- an acknowledgement that the nine other candidates, will, in their views, be only marginal tactors. Moore expects to get about 40 percent of all his votes out of the Northeast-Southeast areas. By contrast, Ray expects to get about 25 percent of his votes from there.

What Ray loses to Moore in the east, he hopes to make up in Ward 3 -- the largely white, upper-income area of the city west of Rock Creek Park Ray strategists expect to wia 75 percent of the votes cast in this area, where Moore and Sizemore usually have run poorly.

Chatman said Moore probably will get no more than 26 percent of the vote in Ward 3. But, he added. "If Doug Moore gets only 10 percent of Ward 3, we're not bothared by it. If the rest of the strategy works, we'll win."

Ray also is hoping to win convincingly in areas of the city where housing rehabilitation is blossoming and newer, younger, more liberal whites and blacks are settling. This includes Ward 1 (Adams-Morgan, Mount Pleasant and LeDroit Park). Ward 2 (Foggy Bottom. DuPont Circle and new Southwest) and Ward 6 (Capitol Hill and near Northeast).

The Ray and Moore organizations differ on how heavy the vote will be in crucial Ward 4. Moore predicts that 14,000 -- more than twice as many as the 1977 special election -- will vote, and 55 to 60 percent of them support him. They are counting heavily on support from the southern areas of the ward, below Missouri Avenue and East of Georgia Avenue, Chatman said. Chatman expects 31 percent of Moore's total vote in the city to come from Ward 4.

Ray strategists are counting heavily on support in the ward's more affluent northern precincts, neighborhoods such as Shepherd Park. North Portal Estates and Fort Totten. Moore has targeted areas where people usually do not vote, Ray strategists say. Moreover, Gay adds, turnout in Ward 4 will probably not exceed 10,000. "There's more apartny in 4 than people realize," Gay said.

The key to Moore's election day strategy is the city's organized labor unions, who, trying to carve a niche in city politics, have endorsed Moore and are running his voter identification campaign and election day operations.

The other candidates in the at-large Council race are Warren A. Hemphill Sr., Hector Rodriguez. H. Chris Brown, Jackson R. Champion, Stuart D. Rosenblatt, David G. Harris, Lin Covington. Richard Blanks Sr. and Frannie Goldman.

The Ward 4 candidates are Mary G. Prahinksi. Malcolm Diggs, Ernest Bowman, Robert V. Brown, Charlene Drew Jarvis, Vickie Street. Richard Clark, Goldie Cornelius Johnson. Andrew W. Coleman, Dorothy Maltsby, Gregory A. Rowe, Nathaniel (Nate) Sims, Norman C. Neverson, Barry Campbell and William Revely.

In the school board race, the candidates are Hilton Cobb. David L. Wellington. Dick Brown, Rohulamin (Ro) Quander, Joseph Webb, Sam Carson. Eugene Kinlow, Vincent S. Jenes, John H. Wallace and Charlotte R. Holmes. CAPTION: Picture 1, DOUGLAS E. MOORE... sympathy and identity; Picture 2, JOHN RAY... the verge of new horizons