What you are describing is the process of creating a new breed or variety. That's how it was done with most breeds, although sometimes chickens create their own new breed through natural selection, without much intervention from people.
Breeders can select for different traits like color, comb...
Crosses can be mixes of any breeds, even bantam breeds, so they can look very different from each other.
A Rhode Island Red is considered a pure breed because it must look a certain way in color and size, among other things.
Your rooster doesn't match the standards for any pure breed, so that...
He's is a mixed breed, meaning he has parents of different breeds. One of his parents could have been a Rhode Island Red, but he is not a purebred Rhode Island Red. Very pretty rooster!