black hole binary

The generally-used meaning of black hole binary (BHB) is a binary star in which a member is a stellar-mass black hole. They are detected by electromagnetic radiation (EMR) (generally X-rays) due to mass transfer or through the combination of orbital dynamics and the stellar characteristics of the black hole's companion indicating an unseen massive object. Such a black hole binary producing X-rays is referred to as active (an active BHB), and one that's not, as quiet or quiescent (quiet BHB or quiescent BHB).

In contrast, the term binary black hole (BBH) is generally used for two black holes co-orbiting. They could be the remnants of a binary star, or could be a pair of supermassive black holes from a galaxy merger (a binary SMBH). A source of detectable gravitational waves is a binary black hole whose orbit has decayed to the point that the two merge (a black hole merger).

Note that these use of these terms is not fully consistent and it is useful to confirm the intended meaning: I have seen each term used with the other meaning.