Some people think that there may be a slight difference. Here is what one book says: 1. I like campING in the mountains. = Maybe you are in the mountains at the time you say those words. Some people think that the gerund is more "vivid" (you can picture it in your mind). 2. I like TO CAMP in the mountains. = Maybe it is just a statement in general about your interests. It is not so vivid. It is more "remote" (not so emotional). Source: Marianne Celce-Murcia and Diane Larsen-Freeman, THE GRAMMAR BOOK.

Although the denotation is the same, there is a slight difference in the connotation. When I hear “I like to walk in the rain,” for example, in my mind the focus, the emphasis, is on what the person likes. When I hear, “I like walking in the rain,” however, I picture the event, the walking in the rain. If someone asked me why I’m studying Chinese, I would respond, “I like learning foreign languages” or “I like knowing about other cultures.” The choice between the two different forms, “like to” and “like –ing” is automatic, of course, and not a conscious thought at the time. I'm thinking about the pleasure of the activity. So the difference is not so much in the meaning as in the usage. This distinction may or may not be felt by others.

To me, a gerund indicates a reality and an infinitive indicates an idea. I like eating healthy food = I already do this. I like to eat healthy food = I don't always do this, but it's still my preference.