BDR-2208: retail package for U.S. (maybe North America in general?). The "BDR-2208" in and of itself is the BDR-208M/E/U, and if you order a "BDR-2208", you get that drive & software. The "BDR-2208"-packaged drive may come with some premium features compared to some of the lineup. But the important thing is that you'd get a BDXL capable drive from the BDR-208 line.
BDR-208: separate drive in the 208 line, maybe with software (depending on vendor), OEM (not retail) package, no BDXL support
BDR-208M/E/U: separate drive(s) in the 208 line, maybe with software (depending on vendor & locale), OEM (not retail) package, BDXL support.
BDR-208D: separate drive, differs from the 208 in DVD-RAM support, no BDXL support.
etc etc etc
They are all models from the 208 line, but some have support for BDXL (and/or DVD-RAM, and/or premium features), whereas others don't. The 2208 package has a different (more feature-rich) drive than the basic 208D. It depends on if you are purchasing a retail package, or a basic OEM package with little more than a bare drive. The different drives/packages are marketed for different needs and different markets.
Except for the few differences, they all share the same features and should share the same quality. Same family, same line, slightly tweaked.