Catenatives followed by infinitives and gerunds

I would suggest that there might be a subtle difference between "I like ski jumping" and "I like to ski jump" insofar as the first conveys a general liking, similar to "I like to watch the sport of ski jumping," while the second seems more specifically engaging, similar to "I like to ski jump on the Matterhorn on clear Sunday mornings."

I think "I like ski jumping" is more ambiguous in terms of whether "I myself" actually engage in the ski jumping activity, where "I like to ski jump" pretty definitively means that "I" am the one who is ski jumping.

In TEFL we teach that there is a subtle difference between, for example: I like to go to the dentist's every six months and I like going to the dentist's every six months. The first, with the infinitive, suggests that I think it's a good idea, whereas the second, with the gerund, suggests that I like the experience.