In linguistic terms, both Fatso and Fatty can be used as names, and written with initial capitals. In addition, fatty can be used as a noun to describe a fat person or dog: "He's such a fatty". These are all usually offensive. Fatty can also be used as an adjective to describe food - I love fatty bacon. This use of the word is not in itself offensive.

Both "fatty" and "fatso" are derogatory, but fatso is slightly more derisive. But they are BOTH mocking.

Ah, thanks Abigail. I think these are not good for friends or others. I just want to know the nuance and your comment, it's very helpful to understand them. No worries, I'll not use it others :)

Fatty can be endearing between family and close friends or to tease/jest. "my little fatty" or "oh, you fatty", if they have eaten your last bit of cake. Fatso is harsher and would be used as a non-abusive insult. I would use neither with people in general. Even with some close friends, I would not use either of these words.