The rule a+b=b+a, for all real numbers a,b, is the commutative law for addition. The fact that we can have g∘h≠h∘g, for some functions g,h, says that composition of functions is not commutative. Composition of functions is not the same as multiplication of functions: f=h∘gmeansf(x)=h(g(x))j=h⋅gmeansj(x)=h(x)g(x).
