The tax-cut bill the Senate Finance Committee sent to the floor yesterday would save the typical middle-income taxpayer an estimated $213 next year, while those in the highest income brackets, over $200,000 a year, would save more than $16,000 each.

In percentage terms, however, the bill would do the same for both groups: lower their tax liabilities about 10 percent.

The committee's proposed cut in the capital gains tax would be the big moneysaver for the very rich.Without it, they would save closer to $4,500 each from the bill. But Republicans particularly defended the capital gains cut yesterday as needed to stimulate lagging U.S. industrial investment. Sen. H. John Heinz III (R-Pa.) said at a Gop news conference that the gains cut would not benefit the rich, but "benefit America."

Republicans hailed the committee's $39 billion bill as a major victory. Senate Minority Leader Howard H. Baker Jr. (R-Tenn.) said it bore "a remarkable similarity" to repeated Republican tax-cut proposals. The rush toward a tax-cut bill this year was started by Republican presidential candidate Ronald Reagan weeks ago.

Capitalizing on the Senate committee's action, Reagan yesterday said President Carter "is clearly out of step with the needs of our nation" in his opposition to an early tax cut.

Sen. Bob Dole (R-Kan.), ranking Republican on the committee, called on the president to "get on the tax-cut train before it leaves the station."

The administration plans to announce its tax proposals, next week. But a high source yesterday said the Finance Committee's bill would cost substantially more than the administration thinks is responsible.

Carter's proposed tax cuts are likely to be worth significantly less than the $22 billion in individual income tax cuts and $17 billion in business cuts and other "productivity" reductions voted by the committee. He also is expected to ask Congress to delay action until after the election.

Dole yesterday called for a tax bill before Nov. 4, election day.

Despite the display of bipartisan unity on the Finance Committee, with only Sen. Bob Packwood (R-Ore.) voting against the bill, there is still some doubt about whether a tax cut will be enacted this year. The opposition from the Democratic majority in the House has not crumbled.

Rep. Barber B. Conable Jr. (R-N.Y.), leading proponent of a tax cut and a member of the Ways and Means Committee, yesterday predicted that increased pressure would lead the House to start work on its own bill. However, he said he believed this would have to be "somewhat simpler" than the Senate Finance Committee's version if it were to be passed this year.

It would "perhaps be possible to bring a somewhat simplier bill, leaving some of the structural adjustments until next year," he said, adding, "The overriding objective is to get taxes down next year."

Ways and Means Chairman Al Ullman (D-Ore.) has put off House consideration of a tax-cut bill until after Labor Day.

The winners and losers table published yesterday by the Finance Committee staff shows that for most taxpayers the proposed cuts would about offset the increase in the income tax burden next year resulting from inflation, plus scheduled increases in Social Security taxes. For example, a typical family of four earning $20,000 a year would be a net $3 a year better off if the bill became law.

For those at the very bottom of the income scale, the tax cuts would not fully compensate for the Social Security increase Jan. 1. But the 90,000 taxpayers in the $200,000-plus bracket would be a net $14,500 a year better off with the capital gains change, and $2,600 better off with just the income tax change.

The committee's proposed tax cuts would be bigger in percentage terms for those at the lower end of the income scale, earning between $5,000 and $15,000 a year. But the 36 percent cut for those between $5,000 and $10,000, and the 13 3/4 percent cut for those earning between $10,000 and $15,000, would still not leave them much better off next year, after the extra tax bite from Social Security and inflation.

Sen. William V. Roth Jr. (R-Del.) said Yesterday that the distribution of the cut would be roughly the same as the 10 percent across-the-board cut proposed by the Republicans earlier this year.

The federal tax paid by an average head of a family earning $20,000 a year would fall from just over 10 percent to 9 percent of that income. The family wage-earner getting $35,000 a year would pay 13.5 percent of that income in federal taxes, down from the present 14.5 percent.

Tax cuts obviously will be an important issue when the presidential campaign gets under full steam in early September.

Although the Repubican members of the Finance Committee paid tribute to their Democratic colleagues on the committe they wasted little time in claiming credit for their party and for Reagan as the one "who lit the fuse" in the tax-cut move.

Reagan said yesterday that he believed that "if this bill comes to a vote in the House and Senate it will pass by a wide margin."