In Milling:
2 Axis, Usually X and Y only.
2.5 Axis 2 Axis With Multipl Z Level Features. Any single feature (pocket island whatever) is at a constant Z level, but there may be multiple features at various z levels. The description of a Mill with a manual quill is good, but the 2 1/2 axis terminology is moreoften used to describe the programming capability. So for example a basic milling software may support 2.5 axis programming.
3 Axis Usually X,Y and Z includes simultanious 3 axis motion. Could be complex surfaces or planar cuts that are rotated out of axis.
4 axis usually incorporates the addition of a rotary table or indexer (B or A axis).
5 axis incorporates both A and B axis. Machine construction varies from simple rotary on rotary to fully articulating heads. In milling the 4th and 5the axis movement is usually defined by A and B axis rotation.
IN 4 Axis Wire EDM:
Uses X,Y and U,V.
X and Y are the lower wire guide axis and U and V are the upper guide axis. Programming the pairs independantly allows for interesting geometric possibilities. Very popular in extrusion die work where a die wants to be round on the entry side and transition evenly into a very conplex shape at the other end.
If you can get a good deal on a half axis, go for it. If you can find 2 of em' you will have a whole axis for a bargain. I will throw in a bag of A.I.R., 2 buckets of propwash and some muffler bearings with mine if you want it.