It would be pretty much impossible to count the number of areas in computer science (CS). There’s no agreed upon way to divide it into categories.
Computer science is the roughly study of
- How to solve problems with computers
- How to model computers theoretically, and the study of those models
This broadly divides CS into the engineering side and mathematics side. (Engineering is the study of how to solve real world problems, and mathematics is the study of models we create). The mathematics side is usually called CS theory. However, this divide is by no means clear, and not everyone will agree with it either.