Isomorphism and homomorphism appear throughout abstract algebra, yet how algebraists characterize these concepts, especially homomorphism, remains understudied. Based on interviews with nine research-active mathematicians, we highlight new sameness-based conceptual metaphors and three new clusters of metaphors: sameness/formal definition, changing perspectives, and generalizations beyond algebra. Implications include a way to articulate a conceptual purpose for homomorphism beyond its relationship to isomorphism: namely, as a tool for changing perspectives when problem-solving. [For the complete proceedings, see ED630210.]