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Morphism is from Algebra/General Mathematics and it is a function that preserves a "structure". (Group Morphism, Isomorphism between sets, etc)

In Graph Theory the terminology is Node and Vertex.

Arrow, Source and Target are from Category Theory.

Morphism is the standard general term. If you have a collection of objects with the some sort of structure then a morphism maps one of those to another preserving that structure.

In CT you usually are dealing with morphisms, but not always and that intuition can get in your way. For this reason, arrow is sometimes used instead to indicate something a little more abstract than morhism.

The term "arrow" is from category theory, not graph theory.