C++ is very popular because of the object orientation. C is a subset of C++.
C++ is a more-modern extension/expansion of C, you really should take the C++ course.
NOTE: The course is likely to teach you the more modern methods. You will have to do some reading on C to learn how to use and recognize the elements that are part of the C subset. I've been reading "C++: The Complete Reference" by Herbert Schildt. The whole first section of the book is dedicated to the C subset. I'm very happy with the book.
C is more efficient than C++.
But of-course C++ is object oriented(OO) language, which supports classes, objects, inheritance, polymorphism, data hiding, encapsulation etc. These are the features of an OO language.
Since C does not have these OO features, it is efficient, and simple. Thats why Microsoft Corporation mostly use C language to bring about efficiency in their Operating Systems(Windows).