Difference between group homomorphism and homomorphism What is the difference between a group homomorphism and a homomorphism?
 A: A homomorphism is a mapping between two algebraic objects which preserves operation in those objects. The object may be a group, ring, field or some spaces or algebras. A group homomorphism is a homomorphism where the objects are groups. 
A: As Samprity describes, a homomorphism is the more general term: it is a function between two algebraic structures preserving the operation(s) defining those structures, and, in general, is structure-preserving. A homomorphism might be a function between groups, between rings, between fields (abstract algebra), between vector spaces, or between two more general structures (algebra homomorphism), which preserves the structures in question. We can also have graph homomorphisms - mapping from one graph to another that preserves the structure of the graphs.
A group homomorphism is a homomorphism, but is specifically describing a structure-preserving function between two algebraic groups.
Given two groups $(G, ∗)$ and $(H, ·)$, a group homomorphism from $(G, ∗)$ to $(H, ·)$ is a function $h : G → H$ such that for all $x, y \in G$, it holds that
$$h(x*y) = h(x) \cdot h(y) $$
