Both leaped and leapt are past-tense and past-participial forms of the verb leap. Other than the spelling and pronunciation, there is no difference between them. Both are old, and leaped was more common in all varieties of English until about a century ago, when leapt became more common in British English. Today, both forms are frequently used in American and Canadian publications, while publications from outside North America tend to favor leapt.
This ngram, which graphs the occurrence of leaped and leapt in a large number of British texts published from 1800 to 2000, suggests that leapt‘s prevalence is a rather new development:
And the corresponding ngram for American texts suggests that leaped still prevails, but not by much:
U.S. and Canada
Former Senator Carol Moseley Braun leaped into the fray with the alacrity of a “Jeopardy!” champ. [New York Times]
Tom, a rugged tomcat, leapt up on another bar stool. [Globe and Mail]
The federal Liberals have leaped from third to first place in voter support in Atlantic Canada. [CBC]
But the escalator jerked to a stop, Humphrey leapt onto stable ground and the woman landed on the steps behind her. [Washington Post]