"Dirty" is a more casual word, while "erotic" is a bit more general and used in academics. For example, art with sexual activity in it would be called erotic. Dirty would be used for things like erotic dancing ("dirty dancing" like stripping) or "dirty talk" (talking about sex with someone you are flirting with)

The intellectual will discuss the erotic life, but in every day lingo some people will refer to sex as "dirty." I would say that if someone talks about "dirty thoughts" or "dirty language" or "a dirty video," they could be full of judgment, responding from a place of shame about the natural body and its pleasures, or they could just have inherited this phrase from older generations or perhaps they are even being facetious. Hard to say out of context.

dirty = disgusting / trashy / filthy. erotic = arousing sexual desire.

A moral judgement.