String/string

what are their diferences?

One is a reference type, the other is a value type. Also, they are a little different in their implementation.

string is the c# alias for the System.String type. It maps directly to System.String and as a result is identical, there is no difference between the two, and they are both reference types.

string is like a c++'s typedef?

ya, i guess similar in concept but i have no idea how c# implements the mapping.

The mapping is built-in into the compiler. It's the same for object and System.Object btw.