I have encountered two definitions of the wedge product. The first is the exterior product as seen on the wikipedia page for "exterior algebra". It is a map $\wedge:\Lambda(V) \times \Lambda(V) \to \Lambda(V)$, so it is defined for pairs of alternating tensors of any ranks.
I have also seen a map $\wedge:A_k(V) \times A_l(V) \to A_{k + l}(V)$ defined for tensors of fixed ranks. I believe this was in Loring Tu's Introduction to Manifolds.
I guess I'm wondering which of these is more common, if they're ever differentiated or if there are commonly accepted names that distinguish the two, and what I should think about when I see $f \wedge g$ somewhere.