Hi Carlos,
This is a difficult one, I will explain it as simply as I can. Using music is the best way to explain it.
The difference between interval and interlude in music is that interval is the difference in pitch between two notes, or the time between notes while the interlude is a short piece of music put between the parts of a longer composition.
As nouns the difference between interval and interlude is that interval is a distance in space while interlude is an intervening episode, etc.
It is complicated, you're on solid ground using interval, this is a much more commonly used term, unless you are a composer or performer in the theatre you're unlikely to need to use interlude.
I hope this helps!!