A supermassive black hole (SMBH) is a very large black hole, generally in the center of a galaxy. A black hole is considered "supermassive" if its mass is on the order of millions (or hundreds of thousands) of solar masses or more, sometimes cited as 108 through 109 as typical (as opposed to a stellar-mass black hole, likely to be about 5 to 50 solar masses). The largest observed as of 12/2019 is on the order of 40 billion solar masses. A SMBH hole has been detected at the center of the Milky Way by observing the tight orbits of stars around it, and it is thought that galaxies larger than dwarf galaxies generally host them. Such large black holes are considered the energy source for active galactic nuclei (AGNs). Some methods of estimating the mass of SMBHs:
A supermassive black hole binary (SMBBH) is a pair of co-orbiting SMBHs. They are thought to result from galaxy mergers.
There is a mystery regarding SMBH formation since the Eddington luminosity would seem to regulate their growth. Current SMBHs have had enough time to grow, but quasars at extreme redshifts suggest a power source that only an SMBH can provide, which would have had insufficient time to grow, and furthermore, there have not been observations suggesting some kind of atypical rapid growth in process.
Regarding terms, SBH is occasionally used to mean SMBH, but perhaps more often to mean "stellar black hole". SMBH unfortunately might be used or read to mean "stellar mass" or "solar mass", but its use as "supermassive" appears pretty consistent.