The Byzantine Kataphractoi are undoubtedly a pretty famous military formation. In games like Civilization V and Medieval II: Total War, it shows up as the Byzantine sort of "special unit." This has generally helped to reinforce an impression in my head that through the various stages of its military, super-heavily armored cavalrymen were one of the mainstays of the Byzantine military.
However, from what I've read from some sources, this might not exactly be the case. Lars Brownworth, in particular, (author of Lost to the West) states that the initial early cataphract units slowly fell out of usage until disappearing entirely in the 7th century, and were only really used in huge amounts during Nikephoros II Phokas' reign here.
I'd like to know from some other opinions here, as I've stated in my question, the extent of the usage of cataphracts as heavy cavalry in the Byzantine military. If the answer to that question is "not much," I'd really like to know what the main form of heavy or light cavalry used by the Empire really was, and how it operated tactically.
The thing that you might be getting confused by is that the actual unit named the "Kataphraktoi" was only used during certain periods. There were many other units of heavily armored tagmata cavalry that went by different names, for example, the Athanatoi of John I Tzimiskes or Alexios I Komnenos, or the powerful Klibanophoroi of Nikephoros II Phokas.
The names often changed from Emperor to Emperor, but I would argue that these super-heavy cavalry were by-and-large equipped in much the same way. The names were chosen by the Emperor to support the tradition of the historical unit, which thereby increased his own authority by tying himself to the elder days of the Empire.