Well, it is a little bit incomplete I think. A pointer contains both the address of a variable and a type. That is why pointer arithmetic works. Without type of pointer, p++ is not calculatable.
The type is implicitly stored as the pointers type. Casting a pointer can change a piece of memory to be interpreted as any type you want. Although the cast might not make logical sense or may even caused undefined behavior in C.
Pointer arithmetic works off of whatever the current type is, as the compiler needs to know how to the memory offsets.