In section 5.1.1 where category is defined the author says
B. for every pair x, y ∈ Ob(C), a set HomC(x,y)∈Set; it is called the hom-set from x to y; its elements are called morphisms from x to y;2
Footnote 2 says
The reason for the notation Hom and the word hom-set is that morphisms are often called homomorphisms, e.g., in group theory.
But morphisms and homomorphisms are different, right ? Morphism can be anything, homomorphisms are more restrictive. Is that correct ? For eg: there can be morphisms between 2 groups that are not homomorphisms, right ?