The term “spatial join” has been coined to describe overlay and similar processes. Basically, spatial joins share the idea of taking two or more spatial datasets, each with associated attribute tables, and creating another dataset. Both the (geo)graphics and the attribute tables in the new set differ from those of the originating datasets.
You find the tools to perform these actions in ArcToolbox: Analysis Tools (for work with feature classes in general).
Union combines feature classes in such a way that the extent of the derived dataset includes the extents of all the constituent datasets. The idea is that, in the union of P and Q to make R, say, the territory covered by R is the territory covered by P and also by Q, including any overlapping territory. In logic, the union of two sets (A and B) is the set of all objects in A or B or both. If A is all red squirrels and B is all squirrels with fuzzy tails, then A union B is the set of all squirrels that are either red or have fuzzy tails or both. The union is equivalent to the logical inclusive OR. (The logical exclusive OR—XOR—would consist of those squirrels that were red or had fuzzy tails, but not those that were red and also had fuzzy tails.)
Intersect combines feature classes in such a way that the extent of the derived dataset includes only the overlapping area of the constituent datasets. The idea here is that, in the intersection of S and T to make U, say, the territory covered by U is only the ...