The other replies concentrate on one difference between the broadband generations: ADSL, adsl2+ and VDSL2. They're right in those descriptions.
There is a further difference that can be implied when talking of a "fibre router": the physical cable connection.
As we understand ADSL service today, the "ADSL router" is actually a combined ADSL modem and a router that understands routing across the modem. A single physical connection exists - the phone line. Most people have stopped calling it a modem/router, and just use "router" as a shortcut.
As "fibre broadband" started up, there was no combined VDSL2 modem/router. Instead you had one box that was a VDSL2 modem (for FTTC) or a fibre NTE (for FTTP), and a separate standalone box as a router. This router has an Ethernet socket for the connection to the modem or NTE, often labeled EWAN. The router sends traffic out using the PPPoE (over Ethernet) protocol, while the modem figures out the stuff specific to the physical copper/fibre line.
So, a couple of years ago, the term "fibre router" meant one with an EWAN connector, that didn't understand VDSL2 at all. It could be used on either FTTC or FTTP.
Nowadays, we are starting to get a choice of combined VDSL2 modem/routers, which work in principle like the equivalent ADSL devices.
So... The term "fibre router" could then be used in the old way to show it has an EWAN connector and you need a separate modem, or could be used in a lazy way for the newer combined devices, where you need a phone line.
For a while, routers with an EWAN connection were more commonly called "cable routers". It was a bit weird buying a cable router to work with your FTTC connection.