But you can tease someone gently, humorously, in a friendly way. In fact, flirting can often involve some pleasant teasing; whereas to make fun of someone is to make them the object of laughter – to make other people laugh AT them, and is less pleasant.
From everything I've read, "teasing" is a way of communicating. It can be positive, negative or neutral.
Making fun of, and bullying are part of a continuum and it is hard to distinguish the effect. But it is easy to distinguish the purpose. Bullying, and to a lesser degree, making fun of, are designed to be hurtful.
We did not make that distinction when I was growing up, and bullying only applied to physical intimidation, not words.