Barely 14 hours after passing the tuition tax credit bill, the Senate yesterday approved a version of President Carter's rival plan for helping middle- and lower-income families shoulder the cost of higher education by expanding existing federal loan and scholarship programs.

The vote was 68 to 28, slightly higher than the 65-to-27 tally for the tuition tax credit bill passed Tuesday night. Carter has said the nation cannot afford both programs, and has indicated that he would veto the tax credit legislation.

"We have shirked our responsibility by passing both bills," Sen. Claiborne Pell (D.R.I.) manager of the White House-backed bill, said after yesterday's vote. Pell had voted against the tuition tax credit.

In the House, Carter's higher education proposal is still pending before the Rules Committee, and will not be considered until after Labor Day at the earliest.

Thus the tuition tax credit bill - passed by the House 237-to-158 - has a large jump on the Carter proposal for helping families pay for higher education. The tuition tax credit bill will now go to a conference committee to work out differences between the House and Senate versions.

The education bill passed by the Senate yesterday was Pell's version of the plan suggested by Carter. The Senate Human Resources Committee reported out Pell's plan - which is slight more generous - rather than the president's. Carter has endorsed Pell's bill.

The major provision of the Pell bill would increase from about $13,000 to about $25,000 the maximum family income level for students eligible to receive tuition grants. The grants would range from $1,800 a year, for students from families earning $6,000 to $250 a year for students from families earning $25,000.

The grant would depend on family income and the amount of disposable income available after the family paid for necessities.

The change would make about 1 1/2 million additional students eligible for tuition aid, with 64 percent of the benefits going to families with incomes of $15,000 to $25,000.

By contrast, the tuition tax credit bill would skew most benefits to families earning $20,000 to $40,000.

The guaranteed student loan program also would be expanded under the Pell bill. Guaranteed loans are available only to students from families earning about $25,000 or less, [WORD ILLEGIBLE] the Pell bill would make the loans available to students without a limiton family income.

Other provisions in the bill would expand the college work-study program and the supplemental grants program.

The major difference between Carter's original proposal and Pell's version passed by the Senate is the way grant benefits would be allocated for families earning between $15,000 and $25,000 a year.

Both plans provided for a graduated scale of benefits, but Carter's version dropped more quickly so that students from families earning about $15,000 or more would be eligible for only $250.

Under the Pell version, a student from an average family of four earning $15,000 would be eligible for a $1,020 grant. A student from a family earning $21,000 would be eligible for $540.

Estimated cost of the Pell bill is $1,46 billion for 1979, slightly less than the $1.7 billion cost of the tuition tax credit plan approved Tuesday night. The House-passed tuition tax credit bill would cost $1.2 billion.

Both Maryland senators, Paul S. Sarbanes (D) and Charles McC. Mathias Jr. (R) voted for the Pell bill, while both Virginia senators, William L. Scott (R) and Harry F. Byrd Jr. (Ind. Va.), opposed.

On the tuition tax credit, Mathias and Byrd had voted for the proposal, Sarbanes against, and Scott was absent.

Sen. Henry L. Bellmon (R-Okla), senior Republican on the Senate Budget Committee, chided his colleagues shortly before yesterday's vote.

"I cannot imagine why we would pass two bills on two consecutive days to accomplish essentially the same objective," he said, adding that the expectation had been that the Senate would choose between tuition tax credits or expanded federal loans and scholarships.