BASIC is a language, QBasic is a compiler.
It is not like the difference between C and C++ at all. It is more like the difference between Borland C++ and C++, or MS Visual C++ and C++. One is a compiler for the language, one is the actual language.
There are many other BASIC compilers, such as:
Visual Basic (yes, this is a BASIC compiler, not its own language)
It is not a waste of time to learn BASIC. Visual Basic is still a very common compiler used in the business world for corporate functions, and if you plan on going into that field, you will use it a whole lot.
Most of the other compilers are not in general use in the professional world, but it would still be good to learn BASIC because it is an easy to learn language that can help you to learn some of the fundementals of programming and can lead you into C and C++.