The Senate yesterday overwhelmingly approved a target 1979 federal budget of $498.9 billion that leaves room for a tax cut $5 billion smaller than President Carter wants, but which, like the president, opposes any changes in Social Security taxes due to take effect next year.

On a 64 to 27 vote, the Senate approved the target budget for the fiscal year starting Oct. 1 that is identical to the resolution reported out by the Senate Budget Committee two weeks ago.

The tentative budget, which will serve as a guide to Congress in approving taxing and spending legislation over the summer, also makes room for an income tax credit for college tuition that has been opposed by the administration.

The Senate budget also adds $1.4 billion to the defense spending request submitted by Carter in his budget proposal last January. The Senate wants an a ccelerated develoment of the MX missile system and increased shipbuilding among other things.

The Senate budget differs substantially in the taxing and defense areas from the tentative plan the House Budget Committee reported three weeks ago and could make for a difficult resolution if the House backs its committjee as fully as the Senate did.

The Senate turned down, 74 to 21, an amendment by Sen. John G. Tower (R-Tex.) that would have added another $1.6 billion to the $129.8 billion defense ceiling the Budget Committee approved. Armed Services Committee Chairman John C. Stennis (D-Miss.) vigorously supported Budget panel Chairman Edmund S. Muskie (D-Me.).

The Senate opted for a smaller tax cut than Carter's in large part because of fears that a bigger budget deficit would contribute to accelerating inflation. It kept the tax cut smaller by postponing the effective date to next January, rather than the Oct. 1 date which the president proposed.

Late Tuesday, only hours after the president declared he would not back off his combination tax cut and "reform" package, the Senate voted to keep the effective date Jan. 1.

Carter has proposed $34 billion in tax cuts to be offset by about $9 billion in revenue raising "reforms." Last week the House Way and Means Committee rejected many of the president's revisions.

The Senate Budget differs substantially from the House Budget Committee version both on the tax side and on defense spending. The House wants to spend $2.4 bilion less than the Senate on military programs, but Muskie noted that pressures are building in the Houe for a substantial increase for pentagon spending.

The House Budget Committee also opposes an income tax credit for college tuition, instead, making room for the administration's alternative: a substantial increase in aid to middle-income college students.

The House takes up its budget resolution next week. Both the Senate and the House are supposed to agree on a tentative 1979 budget by mid-May and by Sept. 15 are to agree on a binding 1979 budget.

The federal budget approved by the Senate last nights calls for spending of $498.9 billion, revenues of $443.3 billion and a deficit of $55.6 billion. The president wants to spend $500.2 billion but, because of his larger tax cut, plans on a deficit of $60.6 billion.The House Budget Committee plans on a deficit of $57.5 billion.

Sens. Paul Sarbanes (D-Md.) and charles McC. Mathias (R-Md.) voted in favor of the budget yesterday, while Sens. Harry Byrd (Ind-Va.) and William Scott (R-Va.) voted against the final budget.