A fundamental property of programming is that you can create an infinite
variation of programs that achieve a given goal. At least as long as the
requirements are written semantically (this is the result we need to
generate) and not with syntactic limits (it must be written this way).
THough you have a syntactic restriction in your definition (we can't
"call" A or B, since you can always replace a call to a function with
the code for that function, and you specified we have the code, we can
use this property.
Now, the question comes down to terminology, if you have multipe ways of
implementing a given algorithm, are they all "one program", or is each
implementation consider a different program.
Normal terminology calls them diferent programs, so your answer is infinite.
There may be a finite (but large) practical limit established by the
language you express the program in, and the machine it will be run on.