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While there isn't necessarily a difference between them, there could be. I like dancing could mean that you get enjoyment out of dancing (doing it) or that you like to watch people dance, while I like to dance only means that you enjoy dancing (doing it). Having said that, in fact, there is hardly ever any difference between the two. After all, I like watching TV and I like to watch TV are the same. I like swimming and I like to swim are also the same.
There are a number of verbs that can take either a gerund (-ing verbal) or an infinitive (to + verb form) as a complement. "Like" is one of those verbs. When a verb can take either complement, the combination with the gerund and the combination with the infinitive can have differing meanings. In some cases, the difference in meaning is subtle; in other cases, it is dramatic.
As a rule, the gerund form will be more real, more concrete, more based on action. The infinitive form will be more hypothetical, more conceptual, less concrete.
I like swimming = more focused on the activity of swimming
I like to swim = more focused on the idea of swimming
With the verb like, the differences are subtle. One could use either to communicate a like of swimming, but the subtle differences are there.