And for places where they can't get LLU set up, they'll be rolling broadband out over Openreach lines rented from BT Wholesale, yes?
They always have to use Openreach lines and (for FTTC) equipment to get to the exchange but after that things vary.
For LLU ADSL the line goes into the CP's MSAN and they arrange for the data to be carried from there. Exactly what route this takes probably depends on the CP. The early part from the exchange is often on BT fibre but with capacity reserved just for them. Some exchanges do have third party fibre in them though.
For LLU FTTC there's something called GEA (Generic Ethernet Access). This is where BT get the data from the cabinet to the exchange then leave you to work out what to plug into the Ethernet socket. From this point on it's going to be the same as LLU but worth noting that unlike ADSL LLU the MSAN is not used to decode the analogue signal. That's all done in the cabinet.
For everything else (ie; not LLU) there are two choices these days:
WBC (Wholesale Broadband Connect)- This is where BT carry your data between the cabinets and your servers.
WBMC (Wholesale Broadband Managed Connect)- This is where they carry your data between the cabinets and one of several nodes scattered around the country. You then arrange to carry it from there to your servers.
I think that's about it :)
As for who does what in this regulator enforced house of cards:
BT openreach - Owns pretty much anything that's physical. Lines. DSLAMs/MSANs, cabinets. If you can touch it it's owned by openreach.
BT wholesale - Creates various products for CPs (Communication Providers).
BT retail - This is the 'BT' that consumers know and love. Or not. The only member of the trifecta that you can actually talk to.
One minor point. With ADSL LLU the CP talks to openreach to get their own MSAN installed in the exchange. They never need to talk to Wholesale. With FTTC CPs always go to through Wholesale. I don't know if it's possible to avoid that for FTTC unless you go with SLU (which means installing your own cabinet and hardly anyone wants to do that).
More info here.