There are many types of mills horizontal, vertical, multi-axis, planar/gantry etc...
A router is pretty much a cheap gantry mill with poor rigidity. Such machines automate work that would otherwise be done by hand with a router.
They couldn't really call them mills because they can't do mill-like work so they just named them routers. Probably the best way to describe a router is that it is designed to handle sheet.
You do get real gantry mills that can do "real" work:
http://www.youtube.com/watch?v=gnt0tTHz ... re=relatedAs you might imagine, they weigh and cost way more.
Differentiating based on speed can be difficult because the fastest machines actually tend to be extremely high speed aluminium mills. I lost the link but there is a video on youtube somewhere of a massive planar mill that goes to 60,000 RPM and looked like it was cutting aluminium at around 200IPM. The chip conveyor was absolutely insane, just a waterfall of metal.
This machine pushes a 1" endmill at 400IPM which is so fast it doesn't even make sense:
http://www.youtube.com/watch?v=XkZIrvsXOVw