Both leaped and leapt are past-tense and past-participle 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 publications, while British publications tend to favor leapt.
Examples
These American publications use both words freely:
Former Senator Carol Moseley Braun leaped into the fray with the alacrity of a “Jeopardy!” champ. [New York Times]
So she leaped at the opportunity to plan the new recycling transfer station … [Wall Street Journal]
But the escalator jerked to a stop, Humphrey leapt onto stable ground and the woman landed on the steps behind her. [Washington Post]
Meanwhile, leaped is nowhere to be found in these British publications:
A teenager who leapt from a car driven by his mother to stab another youth has been detained for four years. [BBC News]
Mr Anstey and his team have leapt on the opportunity the crisis has presented. [Financial Times]
The former Macdonald Cycles employee leapt to fame in 2009 after uploading a video of himself riding around Edinburgh. [Guardian]
Ngrams
This Ngram charts the use of leaped and leapt in British books published from 1800 to 2000. It shows that leapt‘s prevalence is a rather new development.
And this Ngram shows the use of leaped and leapt in American books published during the same period.
