"Milling" and "milling cutters" are correct. The machine can be called a "mill", but if it is a CNC type, it will usually just be called a "CNC".
You can also just use the verb "machine", especially if you're talking about metal. eg. "He machined the part from a steel block".
Edit: I asked somebody who knows better than me - milling and lathing are different things. If the work-piece is spinning, it's lathing, if the cutter is spinning, it's milling.