Here's a quick rundown of the different typed of writable BD media:
BD-R: the basic, write-once BDR media. If you see the media just labeled BD-R, it's probably only a single layer, so about 25 GB capacity.
BD-R DL: the dual layer version of the above, similar to DVD+R DL and DVD-R DL. About 50 GB capacity.
BD-RE: rewritable BD media. Equivalent to CD-RW and DVD+RW or DVD-RW. Typically single layer (25 GB), unless noted as being DL (50 GB).
BDXL: triple- or quad-layer BD-R. Still fairly rare. Somehow works out to 100GB for triple-layer media, or 128 GB for quad layer media. A rewritable version was planned, but hasn't really appeared.
And of course you can buy BD movies, etc, that may be single layer, double layer, or triple/quad layer. (Only very rarely will you find something that is 3 or 4 layers).
As far as I know, a drive must explicitly support BDXL in order to write AND read the 3 or 4-layer discs. But again, most discs top out at two layers.
There is more to be said on the topic, but those are the basics. I'd search for "LTH versus HTL", for example; you'll find that LTH discs are typically worse, but it's good to know what that actually means. It might take a while to wade through all the information out there.