The difference is in the methods used to code a program. C++ is an object oriented language. You can think of this somewhat by looking at a car. A car has parts, such as an engine, gas tank, transmission, wheels, etc. You define each component well, especially the points of interaction, and let the parts communicate with each other ... the car will go.
C is a procedural language. If you want the car to go, you describe each action specifically and in order.;.. i.e. place the key in the slot in the door. Turn right to unlock the door remove the key. lift the door handle and pull the door toward you. Get in the seat. Close the door. Put the key in the ignition. Turn the key .... and on and on.
Most, if not all C compilers will comfortably compile pure C code, as C++ is basically an extension of C. Too, some C compilers use some of the convenience of C++, but they cannot compile C++ code.
C++, if you learn it is a very marketable skill. The C family of languages is quite fast and powerful. Straight C code will typically run faster than C++ simply because it has less overhead. Some say that straight C is more error prone, with memory leaks more likely. Still, if you practice good coding skills, your programs will be quite reliable.