That depends on who you ask. Some sources consider them equivalent. Others use epilation only for methods that remove the root of the hair; depilation is a broader term that includes such methods as shaving. Another difference is that depilation is, in my limited experience (I'm a male with a beard), used much more frequently by people I know who do this sort of thing.
Well I did a quick ngram and it seems that epilation has been consistently more common in English books since 1940, but that doesn't account for regional preferences, etc. I'd never heard "depilation" myself - but then again, I associate "epilation" with removing the root of the hair, and would not include shaving, so maybe I just didn't know what the broader concept would be called!
Oh yes, and in the context of the text I'm editing, by your distinction between these two terms, I need to stick with "depilation", the broader term.