On a very literal level, 抜く means "to pull (something) out," but it's also one of those words that has 15 definition entries in the Japanese-English dictionary, so it can also mean "to pierce; to break through; to go through" (definition #9!), do maybe it's closer to that? Language is weird.
Looking into the term (because I know nothing about swimming 😅), the words freestyle and crawl did keep coming up, so I think they're all the same or at least very similar, yes.