What is the difference between ‎\ldots‎ and ‎\cdots‎?

Although I agree with egreg's comment, the difference is mainly of an aesthetic nature imo. It depends on the context which version to use, which is also how amsmath decides which to use.

Some examples:

a_1,\ldots,a_n aligns better than a_1,\cdots,a_n.

But a_1 \to \ldots \to a_n aligns worse than a_1 \to \cdots \to a_n.

The alignment chosen by amsmath is usually the one commonly found in mathematical articles. However, I guess its not really wrong or anything to deviate from it.