It's the second time I saw this kind of question these two days. They are almost the same. Don't bother differentiate between them if you are not a native speaker.

There's no difference, use whichever one you prefer. Be aware that although "like" can be followed by either the gerund or the infinitive, "would like" (and its contraction " 'd like") must be followed by the infinitive, not the gerund.

The difference between two sentences is what extent you like this. The first sentence means you like tennis but not much (you can play or not, it depends on your feeling), but in the second, when you say: I like playing tennis, it means to say that's your hobby.You like it very much.

Personally, I think they have exactly the same meaning, but 'playing tennis' sounds more casually to me. I'm kind of lazy when I speak so I would almost always say, "I like playing tennis." "To play" sounds more formal or official like a textbook. In formal writing I would probably write "to play". However, I'm sure I use it occasionally in my everyday speech without noticing. Like others have said though, you shouldn't really worry about the differences. ^^