yes, the difference is minute.
but there is a connotation with "I like to go to the movies on saturdays" that i often do go to the movies on saturdays, whereas in "I like going to the movies on saturdays" it is the activity or the idea of going on saturday that i like.
I like to go to the dentist once a year.
When you say like to you mean that you like the idea of doing it, because it is the right thing to do; like going to the dentist. It is sth. advisable, but you don´t really enjoy it.
You use like + ing, when you are expressing an idea you do like:
I like skiing.
It is the same for your example. If you say:
I like to get up early, it means that it is better for you because that way you have time to do more things during the morning. It is useful.
If you say:
I like getting up early, that means that you really enjoy it, maybe because you don't need to sleep very much, and you don´t like being in bed, wasting time.