It's easy to see why people conflate them — both get reduced to a single digit through the same basic digit-sum arithmetic, both can be master numbers, and both get described in similarly grand terms ("your core purpose," "your true self"). The packaging is nearly identical.
The contents aren't. A life path number is locked in by the calendar the moment you're born and can never change under any convention. A destiny number depends on spelling — add a hyphenated middle name or misregister a birth certificate, and the number shifts.