Both leapt and leaped are second and third forms of the verb, i.e. simple past and past participle forms.
Thus, when talking of verb forms of ‘leap’ – you can say-
Leap, leapt, leapt OR
Leap, leaped, leaped
Apart from the spellings, there is no difference in the meaning and usage of these two words – they can be used interchangeably.
Now, coming to which one is the correct spellings – ‘Leaped’ is more commonly used in American English and ‘leapt’ in British English.
For practical purposes, you may use any of them in writing or speech and it would be fine.