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Usually I see the term cataphract when reading books/articles that pertain to the ancient era. In later era's "heavily armed cavalry tends to be used, although it is a vague term.
I have seen some authors use the term for cataphract for Chinese cavalry, but not for periods after the Tang.
The first writer to use 'cataphract' to refer to AoF heavy cavalry was Chris Peers in the Osprey series; in fact I didn't know what a cataphract was until I read his book ten years ago. His choice not to use the same term for Khitan, Jurchen, Mongol, or Song heavy cavalry was purely arbitrary, since they were basically similar to AoF in terms of equipment (full horse armour, full rider armour, lance, single-edged sword, and often a bow). Chronology is not so relevant since the East Roman (Byzantine) cataphracts of the 10th century were about contemporary with the Song and Khitan heavy cavalry.
JiG is partly correct that Roman cataphracts originally had little or no horse armour; those with horse armour tended to be called clibanarii rather than cataphractarii. The true, horse-armoured cataphract only became common in East Roman armies in the 10th century. The Sarmatians, Parthians, and Sassanid Persians on the other hand commonly used heavy cavalry with horse armour, and this is where the Romans got the cataphractarii and clibanarii ideas from. When we use the term 'cataphract' now, we are usually referring to cavalry like that of the Sassanids and 10th-century East Romans, i.e. heavily armoured horse and rider, but using lamellar rather than plate armour.
'Heavy cavalry' is a generic term to refer to any mounted soldier used for charging in formation rather than scouting or skirmishing. The use of horse armour or lances is not essential to classification as heavy cavalry; only the tactical function is. The heavy weaponry and armour of the heavy cavalryman is a result of the function, rather than a cause of it, and is therefore not the key element of the definition.
The ancient Chinese terms that are normally translated as 'cataphract' are
kaima 鎧馬 ('armoured horse') and
tieqi 鐵騎 ('iron cavalry').