These are very similar expressions. For a non-native learner, you can probably use them interchangeably. However, since you asked about the difference between them, I will try to explain how I use them differently as a native speaker. A) “I like to go skiing” B) “I like skiing” or “I like to ski” A means that I like the whole experience - going to the hill, skiing down the mountain, riding the chairlifts, sipping cocoa in the lodge. I like the whole package. B means I like the part where I’m actually skiing down the hill. I like the actual verb of skiing. A) “I like to do yoga” B) “I like doing yoga” A means that I like I go to yoga class and have the experience and get the benefits of yoga. B means I like what it feels like when I’m actually doing the yoga and feeling the stretch. I hope these examples clarify the subtle difference. But for common usage, you can use either.

Do in "Like to do" is a verb and noun in "Like doing".