Taking away the CNC element, it might depend on what era you were from? It could be argued that size of the machine, materials or dimensional capabilities denote the difference? Even the method of holding onto the tool or workpiece? But now there's more overlap between them almost every day. 2d, 2.5d. 3d? There's probably exceptions to all those.

Traditional milling machine would be bigger and heavier, certainly used for metals, exclusively hard metals in the machine shops I was in as a lad. (at tea break, you could start reading the paper but you couldn't sit down until the bell went! all dressed in white lab coats too. LOL)

Historically routers were for wood but now you have small milling machines and large routers... both capable of machining many materials...

I'm sure there are other definitions too, depends where you are coming from what facet you see.