If you are talking about something other than people, they mean the same thing and are interchangeable. If you are talking about people, though, there is a cultural difference. I could say I am fond of a relative - a niece or nephew, say. I could also say I am fond of a woman if I meant it romantically. However, I would never say I was fond of a colleague at work. People would look at me a little strangely. If I said I liked that same person, it would sound perfectly natural. 'Fond of', applied to people, implies a closeness that 'like' does not.

There is not much difference. I like apples. I am fond of apples. They both mean essentially the same thing. The main difference is a difference of style or mood. I "like" apples is simple and direct. I "am fond of" apples sounds a bit more personal or emotional.