You are correct in your observation that object-oriented programs are based in many ways on the procedural paradigm. You are also correct in that syntactically all that really happens is that you invoke functions. In fact, you could implement many features of object oriented languages using procedural mechanisms (e.g., function pointers in C++). You could thus do an object-oriented design and still implement it in a procedural language (e.g., like old C++ compilers did).
The importance of the object oriented paradigm is not as much in the language mechanism as it is in the thinking and design process. In procedural programming the thinking is about operations and breaking those operations down using other operations, grouping them into modules, etc. This means that the data or state falls into a secondary importance. It is like thinking of mathematical operations.
The object oriented paradigm, on the other hand, says that you need to think of state and operations together as an entity, and then design your program as interactions between entities that exchange state and activate operations.
