You asked another great question. Mathematicians like to classify numbers into many different groups so they can study numbers with similar properties more carefully. But there are also many other ways to subdivide the real numbers. There are 2 big important subdivisions of the real numbers. The set of integers lies within the set of rational numbers.
Integers are just positive or negative whole numbers.
Those are the major subdivisions that mathematicians like to look at. Each of the above groups of numbers has special properties unique to it. This idea of having sets within sets within sets, etc. is quite prevalent in mathematics. There is a whole area in math called set theory that deals with all kinds of sets. Group theory, ring theory, and field theory use many of the same ideas, too.