They are more or less synonyms and the meanings overlap.
"Mock" often includes the idea of exaggerated or distorted imitation. Mockery is always cruel. The idea is to get other people to see the victim's speech or body language as being ridiculous or funny.
"Teasing" often (but not always) means tormenting someone by making them think they are about to get something they want, then yanking it away at the last instant. If you happen to know the comic strip "Peanuts," by the late Charles M. Schulz, there is a running joke. Charlie Brown always wants Lucy to hold an (American) football for him so that he can kick it. She teases him by making him think she will do it. Then the yanks the ball away at the last instant.
"Ribbing" or "kidding" means a friendly insult. It is sometimes a way men can express affection without danger of seeming effeminate.
"Well, Sam, look at that! Darkening our door again! You just keep turning up like a bad penny!"
"Yeah, Phil, good to see your ugly old face again. I assume you are still misbehaving as usual?"
In the United States today, we would be more likely to say "kidding" than "ribbing."
Bullies, of course, will give someone a real insult, and then lie and say they were "just kidding." "Aw, I was just kidding, lighten up, can't you take a joke?"