Should we merge them?
I would say applications of graphs in CS do not fall in under graph theory as a mathematical field (research area), e.g. all the A* questions should be labeled
On the other hand, questions regarding graph classes and their complexity (recognition, modification, operations etc.), as well as classical problems like chromatic number etc., should possibly be
That said, the distinction is rarely interesting here at cs.sx.
Therefore I vote yes: merge.
... graph theory is the study of graphs, ...
I don't think there is any difference between "graphs" and "the study of graphs".