This is a semantic question.
A renormalization scheme is nothing more than a renormalization procedure. For example, Minimal Subtraction and momentum-space subtraction (subtraction for given values of Mandelstam variables) are examples of different renormalization schemes.
Renormalization prescriptions are often used to distinguish between two different subtractions points in momentum space (two sets of Mandelstam variables) within momentum-space subtraction. For example, one can sometimes make use of a prescription such that the renormalized mass is equal to the physical mass (on-shell prescription) whereas for other problems subtracting a diagram at $p=0$ can be more convenient. One can think of different prescriptions as different initial conditions.