I think the main difference is that in the mill the router stays in a fixed position and the workpiece is moved. In a CNC router the workpiece is fixed and the router is moved.
CNC routers are in general for lighter work and only soft material and the bit is usually rotating at very high speed. A mill is in general much stronger, can rotate also with low speed, can take deeper cuts and can mill not only soft material but also hard materials, even metal.
CNC mills are also available in the market. Often a bit heavy on the wallet though. However you can buy CNC add on for the Proxxon mill for rather small money (original proxxon CNC is more expensive than unoriginal. for instance thsi kit is low cost
http://www.ideegeniali.it/shop/31-proxxon-mf70-retrofit-kit.html I do not have any experience with it myself.
There are even cheaper kit with smaller torque/ motors in the market but as far as Im' told these are pretty much useless.
Also be aware that for CNC you also have to buy several pieces of software. If you want to do something in the advanced end the software can be very expensive.