How many kinds of CNC milling machine have?

Just two. Ones that work. Ones that don't work.

There are several general "classes" of milling machine, each made in vast ranges of sizes by many different manufacturers.

Table type - the whole workpiece sits on the machine and is moved around in two, three or four axes (x-z, x-z and rotation, x-y-z, x-y-z and rotation).

Floor type - the workpiece sits on fixed foundation plates (on the floor) and all the movements are done by the machine axes, with the machine column moving along a bedway.

Planar type - the workpiece is on a table that moves in one axis under a rail that carries the cutting head

Gantry type - the workpiece on a fixed foundation plate and the machine built as a "moving bridge" that travels over it.

Plus variations like lathes and vertical borers that have live tool milling capability...


Example photos (not all CNCs, but the machine types are similar whether manual or CNC):
A Table type horizontal spindle machine:
http://mudar-m.com/html/img/product/100/13539473011474262885.jpg

Floor borer:
http://www.electromotion.co.uk/data/stockattachments/machine-tools-borers-floor-borers-juaristi-31681-img03-lrg.jpg

Planar miller with both vertical and horizontal spindles
http://www.fortunepacific.asia/photos/pro/Planer-Type-Milling-Machine_PM1000-X.jpg

There are many different types and brands of CNC milling machines.
Sunstrand, Tree, Brown and Sharp, Shetaki, Okabi, Mitsubishi, Toyota... each one is unique.