The Senate last night passed a binding 1979 budget that is about $7 billion smaller than President Carter's revised, mid-year budget request and about the same size as the one approved by the House last month. The vote was 56 to 18.

The Senate defeated several attempts to cut spending even more. The Senate version, which must go to a conference with the House, is $9.3 billion smaller than the tentative 1979 budget Congress agreed to last spring.

The Senate budget is $489.5 billion for fiscal 1979, while the House version is $489.8 billion.

Both the House and Senate budgets more than fulfill the Carter administration's request that Congress cut federal spending in 1979 to about $491 billion. Carter made the request, in the interests of fighting inflation, only days after he announced a revised 1979 budget of $496.6 billion.

When the federal government runs a deficit it borrows from the public, in competition with private borrowers. That has the tendency to boost interest rates, especially in times like today's when demand for credit is heavy.

The resolution also leaves room for a tax cut of $15.2 billion in fiscal 1979, which starts Oct. 1, and a continuation of $8.2 billion of tax credits that were enacted into law in 1975.

The House version leaves room for about $16.2 billion of tax cuts - the amount specified in the tax bill passed last month by the House. The Senate Finance Committee begins work on its version of a tax cut bill today.

Because the fiscal year starts Oct. 1 and the tax cuts become effective on Jan. 1, the Senate budget resolution accommodates a tax cut in the neighborhood of $19 billion in calendar year 1979.

The deficit under the Senate version will be $42.3 billion, $6.2 billion less than President's mid-year estimate and $8.6 billion smaller than the resolution Congress passed last spring.

Sen Edmund S. Muskie (D-Maine), chairman of the Senate Budget Committee, said the binding budget - which can be exceeded only be special vote of the Congress - takes " account of the two major changes which have occurred in the economy" since the spring budget was formulated, lower unemployment than anticipated and higher inflation.

The Senate defeated an amendment by Sen. William Proxmire (D-Wis.) to reduce future spending by $17 billion and an amendment by Sen. William Roth (R-Del.) to cut 1979 spending by about $10.1 billion.

The Senate also rejected an attempt by Sen. Harry F. Bryd (Ind.-Va.) to cut $2.4 billion from spending on international affairs and Sen. Patrick J. Moynihan (D-N.Y.), withdrew his amendment that would have added $400 million to the budget to provide fiscal relief for local government.

The House and Senate will meet in conference Friday to iron out the differences - most of which are minor - between the two budget resolutions.