OK these are all types of speaking, but they depend on who's talking and who's listening.
If I "SAY" something, nobody has to listen. I can say right now "I love ice cream" and nobody is listening, but I still said it.
"If I "TELL" someone I like ice cream, then I'm saying it and somebody is listening.
"Talking" is a broader verb, but it can include saying and telling. "I'm talking to myself" means that nobody is listening but I'm talking. If my friend and I are talking, we're having a conversation.
Chatting is like the above example of my friend and I talking. Chatting is like a small conversation. "We were chatting in a cafe for a half hour."