What's the difference between the two? Can you plug for example a ADSL
broadband line into a Cable router? I mean, they both have an ethernet port
A router must have at least one LAN port and one WAN port.
Port could mean an ethernet jack or it could mean a logical
connection to a modem built into the same device. If there
is a modem built in then technically it is not just a
"router" anymore, more often it would be called a modem or
modem/router as the router is the secondary device added so
the customer can use the modem with more than one computer
without having to buy more equipment to do so, in order to
have NAT functionality from the modem hybrid device.
If the router has an ethernet WAN port, it is not
necessarily an ADSL or Cable router, it is a universal
router that can be used by either broadband type once you
plug the needed type of modem into the router's ethernet
port.
If the router does not have an ethernet WAN port but instead
has the internal modem, the type of modem it is determines
which type of broadband service it can use.
If the router has both an internal modem and a WAN ethernet
port, it would seem there would have to be a setting in the
router control panel to set whether it considers the modem
or the ethernet port to be logically considered the WAN port
that is active.