Lr Classic is a desktop version, but is part of the CC plan. Not a standalone. I don't think you can get it alone.
Lr CC is now a whole "ecosystem" as Adobe calls it, an online sharing, storage and editing service. Sorta like Mylio but with included online storage.
I dunno if you can buy more than 1TB. I imagine lots of folks will be putting only their working, sharing and gallery photos there, although if you do a lot of weddings, etc I could see how that would fill. Esp since it holds raw. Wonder if it does HEIF.