The GNAT model of compilation is close to the C and C++ models. You can think of Ada specs as corresponding to header files in C. As in C, you don't need to compile specs; they are compiled when they are used. The Ada `with' is similar in effect to the #include of a C header.
One notable difference is that, in Ada, you may compile specs separately to check them for semantic and syntactic accuracy. This is not always possible with C headers because they are fragments of programs that have less specific syntactic or semantic rules.
The other major difference is the requirement for running the binder, which performs two important functions. First, it checks for consistency. In C or C++, the only defense against assembling inconsistent programs lies outside the compiler, in a makefile, for example. The binder satisfies the Ada requirement that it be impossible to construct an inconsistent program when the compiler is used in normal mode.
The other important function of the binder is to deal with elaboration issues. There are also elaboration issues in C++ that are handled automatically. This automatic handling has the advantage of being simpler to use, but the C++ programmer has no control over elaboration. Where gnatbind might complain there was no valid order of elaboration, a C++ compiler would simply construct a program that malfunctioned at run time.