Amtrak yesterday took a major step toward reviving the passenger and auto ferry service between Washington and Florida that was provided by Auto-Train Corp. before it went out of business in 1981.

Amtrak asked the U.S. Bankruptcy Court in Washington to approve a plan for Amtrak to buy Auto-Train's name and its 19.8-acre terminal at the southern end of the line in Sanford, Fla., for about $2 million.

Officials at Amtrak said that the federally subsidized railroad hopes to begin service between Sanford and suburban Lorton, Va., by the end of October.

Auto-Train Corp. filed for reorganization in bankruptcy and then went out of business two years ago. Since then, bankruptcy trustee Murray Drabkin has been cleaning up the railroad's finances and trying to raise money to pay creditors.

The agreement between Amtrak and the Auto-Train trustee provides that, when the service starts, Amtrak will give special discounts to Auto-Train customers who paid for tickets on the old service, but never received either transportation or refunds.

"We want to make amends" to the former customers, said Amtrak spokesman John Jacobsen.

Auto-Train's name "was important to us because it is . . . locked into people's minds as auto-ferry service between Washington and Florida," Jacobsen said. "To call the service by any other name would be confusing and take time to win public acceptance." "We want to hit the ground running with this new service," he added.

Amtrak already has made lease arrangements for the Lorton facilities and also has bought enough rail cars to carry the autos to and from Florida, Jacobsen said. Amtrak is building the passenger cars for the service. Total start-up costs are expected to be betweeen $3 million and $4 million.

Amtrak will pay $1.75 million in cash for the old Auto-Train assets and also will forgive about $100,000 in debts owed Amtrak by the defunct railroad. The agreement with Amtrak reduces only a small portion of Auto-Train's debt, said Drabkin.

Auto-Train Corp. was at least $20 million in debt when it filed for bankruptcy, said Drabkin, a member of the law firm of Cadwalader, Wickersham and Taft, who was appointed by the bankruptcy court as trustee for Auto-Train.

Despite Auto-Train's heavy losses, Amtrak officials say they are confident they can run a profitable car-ferry business.