FTTP, I believe, I won't pretend to know too much about the difference between the two..
FTTC - fibre to the cabinet (a green roadside box somewhere not too far from you); speeds up the link from the exchange, but the last part of the connection to your house - for broadband and 'phone - uses the original copper wire. Confusingly, called "fibre" by many in the industry.
FTTP - fibre to the premises: actual fibre all the way to your home. Involves a new hole in your wall, and a different piece of equipment (O something - OTC is it?) on the end of it, which you'll use with your existing router (if a hub 2; not sure about earlier models). Called "full fibre" - the "full" is important - by many in the industry. You won't get any landline 'phone service over such a connection; not sure if you can keep that over the old connection (pretty sure you can't with PlusNet at least, as any change, as opposed to continuation, they remove the landline part, and changing to FTTP certainly counts as a change). [With PlusNet, start looking into VoIP with someone else - such as A&A or voipfone - anyway, assuming you want to keep a landline-like service at all; many people don't. Really only needed if you have lots of people - elderly relatives or some elderly companies! - who only know your old landline number, and don't use a mobile much.]
