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=related
As 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