Ugh. Sorry to hear.
Short block - engine block, crank, pistons. No accessories.
Long block - block, heads, oil pump, oil pan, filter housing, maybe water pump. No accessories such as a/c compressor, steering pump, starter, headers, etc. IOW, a bare bones engine. Everything to make it fire and run needs to be bolted on.
Reman means its been disassembled and put back together to factory specs. Critical parts such as bearings are typically new. Major components if they meet factory tolerances are cleaned and reused.
Essentially a rebuilt engine.
I don't know if BMW rebuilds these motors themselves or farms them out to a competent sub contractor.
More recently, I bought calipers for my E36 M3 race car which were considered factory new, but upon closer inspection I could tell they were clean cores with fresh everything. I'm sure BMW didn't rebuild them or ATE for that matter but a qualified subcontractor. Important thing was that they felt new, installed new and worked like new, even on a race level shake down.