You are asking what is the difference between a present participle and an infinitive. This is one of the two or three most common questions on iTalki. Different people explain it in different ways. I'll give you my way of seeing it, but other people will have other ideas. The infinitive is simply the name of a verb. It adds nothing at all to the meaning of the verb. It doesn't need to be interpreted. For that reason, it is useful for stating direct truths and facts. For example, "I am afraid to swim" simply means what it says. It requires no interpretation. "Afraid to swim" describes the subject of the sentence. Present participles are different. They are not facts. They are like PHOTOGRAPHS. "Swimming" creates an image in your mind. You can imagine it happening. "To swim" does not create any such image. It is just a verb. You can look it up in a dictionary and you know everything about it. But "afraid of swimming" means seeing that photograph makes you afraid. It means you are afraid of the IDEA of swimming. It might mean that you are afraid that other people you know might swim. It very well might also mean that you yourself are afraid to swim. But you might not be. Here's another example. Many people are afraid of flying, but most do it anyhow. The idea of flying makes them afraid, but it does not stop them from doing it. However, someone who is afraid TO FLY does not fly. The infinitive means EXACTLY what it says. "Afraid to fly" states a fact that does not request to be interpreted.

I can't think of any real difference.

The meaning is the same, just two slightly different ways of saying something. ex) She is afraid of doing something wrong so she has chosen to not do anything. vs She is afraid to do anything because it might all be wrong. In spoken English, which one to use is a matter of personal preference. Choose what is easiest for you and go with it :)