Physicists often talk about a vector representation. For example, the first comment to this answer says:
That the $(1/2,1/2)$ representation corresponds to a vector irreducible representation of the Lorentz group is not obvious.
From a mathematical point of view all representation are valued in vector spaces so it's somewhat confusing to talk of vector representations. That is all reps are
$G \rightarrow Aut V$
Where $V$ is some vector space.
My first inclination is that it's simply a physicists way of speaking to distinguish between spinorial reps (which, rather than going from G, goes from the universal cover of G, which in the case of the Lorentz group is its double cover) and ordinary 'vector' representations, which goes directly from G.
Is this on the right track, or is there more to calling a rep, a vector rep?