They are sometimes but not always interchangeable. Try to think of 'within' as meaning 'not passing beyond the borders/limits of' something.

Hello there :) Within and inside are generally interchangeable in whatever context however 'inside' is usually more common whilst 'within' can be regarded as quite formal. For example: 'The cat is inside the box' - 'The cat is within the box' Both mean precisely the same thing, however 'inside' does sound more natural. I hope this helped! :)