I have no idea if there’s a rule. My friend Nacole shared this take on it:
Here’s my hypothesis:
If you “finish” something, it sort of ceases to exist in your reality – you finish your dinner, or you finish a race.
“Completing” something results in a product of some sort that you keep – you complete a painting. You can also complete a marathon, which is an accomplishment that stays with you forever (maybe that’s a stretch.)
If you “finish” a book, I take that to mean that you read the whole thing, and probably won’t read it again.
If you “complete” a book, it sounds to me like you have reached the end of the writing process, so for the rest of your life you can say “Hey! I wrote a book!”
Of course, this is the English language, so there are exceptions. In fact, there are probably more exceptions than examples of the rule. Also, we haven’t discussed “I’m finished” versus “I’m done,” but that might just be a regional Texas thing.
I have now finished thinking about this issue, and I’d say this post is complete.