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A binary black hole (BBH) is a pair of black holes that are co-orbiting. The LIGO/Virgo GW detections confirmed the existence of such pairs of stellar-mass black holes. Analogous pairs of supermassive black holes (SMBHs, i.e., binary SMBHs) are also possible, a presumed result of galaxy mergers.
In contrast, the term, black hole binary (BHB) is generally used to indicate a binary star in which (at least) one companion is a black hole.
With the advent of a catalog of gravitational wave observations that indicate black hole mergers, there is now observational data for study. The masses of the black holes are not quite what was expected: some a bit larger than expected for stellar BHs (though much smaller than SMBHs). This has some effect on theories of mass limits on stars, their post-main-sequence, evolution, including the final core collapse. The observations also bring up the question of by what mechanism two black holes came to be co-orbiting, the possible mechanisms termed binary black hole formation channels, one being that they result from main-sequence companions (i.e., the isolated formation channel), the other that the black holes were formed separately and formed a binary through capture (i.e., the dynamical channel). Of interest are the relation of their rotation axes, something that the GW detections reveal, at least to some extent. Simulations, e.g., of globular clusters, are carried out to attempt to explain the demographics observed so far.
Note that the terms binary black hole and black hole binary are not always used with the above-mentioned specific meanings and it is best to confirm the intended meaning.