ATLANTA — The N.C.A.A. Board of Governors, under increasing pressure from legislatures around the country, voted Tuesday to pave the way for college athletes to profit off their fame, but the decision came with an elephant-size caveat: Any policy changes must maintain clear distinctions between amateur athletes and professional ones.

The vote was a surprising turn by the N.C.A.A., which for years has resisted calls for athletes to be compensated for the use of their names, images and likenesses. The board was responding to a report from a committee studying the issue and was expected to do little more than give the committee extra time to do its work.

The N.C.A.A. president, Mark Emmert, acknowledged that the passage of a bill in California that would permit sponsorships, the emergence of more than a dozen others like it nationwide and calls for change from prominent athletes like LeBron James had nudged his organization into action.