"Ancient" means "very old." "Primitive," on the other hand, implies that something is very "elementary," "basic," "not advanced," and so it could have a negative connotation. For example, if you say the Martian civilization is very ancient, you just mean that it is a very old civilization (and this may even have a positive meaning, in the sense that it has survived for a long time and advanced over the ages). On the other hand, if you say that "the Martian civilization is very primitive," you are saying that the civilization is very basic, crude, and not advanced. So ancient = 古老 and primitive = 原始。

primitive --- simple ancient --- old