The Senate Finance Committee yesterday approved a version of President Carter's proposed "wind-fall profits" tax that would collect only half as much as Carter proposed or as the House voted last July.

The new tax, which the panel weakened with numerous exemptions, would bring the government an estimated $141.7 billion in new taxes between now and 1990, compared to $273.4 billion in the House bill and $292 billion sought by Carter. These revenue estimates are higher than some made earlier; they assume higher oil prices in the future.

About 60 percent of the money would be placed in trust funds or otherwise reserved -- $15 billion for mass-transit grants and $70 billion for cash grants to help the poor pay fuel bills and for a tax credit for middle-income users of home heating oil.

The panel also approved $21.5 billion worth of tax credits for home-owners and businesses to spur conservation and the use of new forms of energy. The remaining $35.2 billion would be available for other new energy programs or whatever else Congress chose; it would simply be increased federal revenue.

The bill contains these major provisions affecting consumers:

Cash grants of up to $400 a year for welfare and food-stamp recipients to help offset the recent sharp rise in heating oil prices, which have doubled in the past year.

A new tax credit of up to $200 a household to help middle-income homeowners and renters who heat their houses with oil, propane or Canadian natural gas.This credit would go to families earning $20,000 a year or less.

A new, higher $5,000 tax credit for homeowners who install solar, wind-powdered or geothermal equipment, and extension of the existing $300 home insulation tax credit to apply to heat pumps, wood stoves and replacement furnaces as well as to less exotic items such as storm windows.

The administration's proposal was designed to recapture for the treasury part of the "windfall" that the oil companies are expected to reap bcause of Carter's decision to decontrol oil prices and because of recent price increases by oil-exporting nations.

Between now and 1990, those factors are expected to increase industry revenue by $893 billion before taxes. The oil companies would pay $388 billion in extra federal income taxes on this amount.

That would leave $505 billion. Using that estimate, the Finance Committee bill would impose an effective tax rate of just over 25 percent on the windfall the industry is expected to receive, compared to 50 percent for the House bill and 52 percent for Carter's proposal.

Moreover, the Finance Committee bill would begin to phase out the windfall tax in 1989 and eliminate it entirely by 1992. Carter had asked that the tax be made permanent to recapture part of any future windfalls.

Even the president's version of the proposal, which actually amounts to an excise tax imposed on each barrel of crude oil, was regarded as mild. There were charges that Carter was using the measure to allay criticism of his decontrol decision.

Although Carter said yesterday he was "pleased" that the panel had completed the bill, the administration is expected to try to toughen the legislation when it reaches the floor, probably early in November.

There were indications yesterday that the bill could become mired in lengthy debate. Sen. Mike Gravel (D-Alaska) reportedly is likely to try to filibuster the bill, and several senators want to increase the tax credits.

Yesterday's vote came after the Finance Committee defeated, on a 10-to-10 tie, a GOP-sponsored proposal that would have frozen Social Security taxes at 1980 levels, blocking a large increase now slated for 1981.

Sen. William V. Roth (R-Del.), sponsor of the provision, had argued that at least some of the windfall revenues "ought to be returned to working Americans" in the form of a tax cut. The panel deferred the issue to next January.

The committee is scheduled to meet next Wednesday to reconsider several relatively minor issues, including possible modifications of the formula it approved for allocating grants for the poor among states.

However, committee Chairman Russell B. Long (D-La.) won agreement from members that none of the major elements of the bill would be reconsidered. The measure was approved, 11 to 1, with only Gravel dissenting.

The huge revenue estimates for the Finance Committee's bill stemmed from last-minute revisions in assumptions about the price of oil in coming years, made in part to prevent an early phaseout of the tax.

Under an ammendment added by Sen. Malcolm Wallop (R-Wyo.), the windfall tax would begin phasing out as soon as the U.S. Treasury had received 90 percent of projected revenues.Under the panel's earlier projections, that would have happened in 1983.

The cash grants and home heating oil tax credit that the panel has approved for the poor and middle-income households actually would amount to $30 billion, less than half the $70 billion set aside in trust.

The remaining $40 billion still would remain in reserve for these purposes. The committee is scheduled to reconsider the question of aid to the poor Wednesday, and may increase the $30 billion package.

Despite the sharp cutback from the House version of the bill, analysts said the White House may not fare too badly when the measure reaches a House-Senate conference committee.

Long is expected to scrap some tax credits.

Nevertheless, the Finance Committee measure deals the White House one additional setback by repealing a key provision of the 1976 Tax Reform Act that Carter wants badly to preserve. Congress had deferred the provision twice.

The provision, known informally as the "carryover basis" law, would increase capital gains taxes on the profits from the sale of inherited assets. Conservatives have argued vigorously that the measure should be repealed.

The Finance Committee bill would slash the windfall tax voted by the House last summer by exempting from the levy several major categories of oil -- newly discovered oil, hard-to-recover oil, independent small-well oil and so-called heavy oil, to name a few.

Yesterday, the panel added a rider by Wallop that would reverse a decision by the House to allow oil companies to claim a percentage depletion allowance on any windfall they may incur. That would cost the Treasury $3.7 billion over 10 years.

The $21.5 billion in tax credits the committee included involved $8.3 billion for homeowners and $13.2 billion for business. Carter has proposed a far smaller tax credit package, but it is tied up in the House.

The committee's proposal for aid to the poor would channel the extra grants to welfare and food-stamp recipients simply by increasing their regular government checks. However, states would have the option of using the money for their own fuel aid programs.

The aid would be allocated on a state-by-state basis using a complex formula that takes into account the number of cold days and poor persons in an area and the amount of energy used by households.