That's a very good question. With karate you can say, "I practice karate" because it's a martial art, a discipline. With swimming you can say, "I swim." Just like that.

For swimming we just say "I swim" or I "go swimming. For karate, we "practice karate" or "do karate" Here's a good website to help you distinguish when to use each verb: http://www.englishteachermelanie.com/vocabulary-verbs-used-to-talk-about-sports-play-do-go/

In English, it is "I swim" and "I do karate" (or "I practice karate"). I think, in general, that in English we only "play" team sports and not individual sports - so it's I jog, I walk, I swim, I ski (but not I play jogging, I play swimming, etc).