Thought Id mention this, as its something that kind of creates some confusion when trying to answer questions, and in many cases, it adds some confusion and requires more questions before one can answer.
CNC - Stands for Computer Numeric Control. You can have just about anything CNC - CNC sewing machines, Lathes, vacuum cleaners (iRobot) etc... heck... a printer is CNC as is a laser engraver. So, keep in mind that a CNC is only a method of control.
A Mill - the spindle turns the tool, and the tool cuts on stationary material (as in not spinning). A router is also in the same family. One would use a mill or router to do things like cutting sound boards, engravings, making pockets (like in a box call), drilling patters, and making non-cylindrical parts. Generally the hobby machines are referred to as "CNC Mills" and when you get to the professional/industrial machines, they will usually be called Vertical Machining Centers (VMC's).
A Lathe - well, you know what a wood lathe does... the tool is stationary and the spindle spins the material. With a CNC lathe, its usually based on the premise of a metal lathe. The difference from a wood lathe most are familiar with is quite big. Even if you leave out the computer control part, they are different. With a wood lathe, you hold the tool, and can position the tool how ever you want as youre using it. On a metal lathe (and CNC), the tool is hard mounted to the machine, and can not be repositioned while in use. The tool moves in two axi (Z - towards and away from the face spindle axially, aka length, and X which is towards and away from the spindle radially, aka diameter) but you cant rotate the tool to get into a little nook or cranny - its hard mounted. So each feature has to be either planned around the tooling, or add tooling to come at one feature in multiple ways to make it possible. Generally the hobby machines again are referred to as "CNC Lathes", but in contrast, so are the professional/industrial machines... but youll also find the industrial machines referred to as Turning Centers.
So in the process of "CNC'ing" an entire AR or RF style duck call (at least as far as Im familiar with them)you would use both a CNC Lathe and a CNC Mill. The CNC lathe would turn the parts, both barrel and keg (insert). The CNC mill would cut the sound board.
Of course there are always exceptions to the rule... and ingenuity is the only limiting factor. ( I know guys that make calls on a CNC mill - its a slower process but completely doable). But generally speaking - to make an entire call, yould need both.
Also, a common misconception is that a 'CNC' is something you stick a piece of material in, press a button, and magically have a call. Which is not true. You have to tell the machine specifically what to do, when, the order, how fast, etc... So just like any other computer - Garbage in, Garbage out. One of the ways I look at it is... A VMC and CNC Lathe is to a call maker - as - a Computer and printer is to an Author. Nothing happens without someone at the controls. One can create unique works of art or mass produce something of their own design/idea with them or they can plagiarize another and put their name on it. So, like so many other things... its the "man behind the curtain". I know not everyone thinks its magic... but without knowing more about it, it can sure look that way. SO I thought Id mention that for those that dont know anything about it.
Hope that give you a little more info on the types of machines.
Cheers
Wade