I understand that there is a difference between the two, but I'm still confused. Are the terms "ostinato" and "motif" interchangeable?
No. An ostinato is a sustained pattern, lasting many bars. A motif is a particular 'musical idea', that may itself last several bars, which keeps re-occurring during a piece.
An ostinato is particularly a rhythmic pattern that is repeated bar after bar, or in two or four bar sequences. A motif will pop up from time to time to remind us of itself.