So, first off, kataphraktoi are just a type of heavy cavalry, the same as knights, cuirassiers, etc.

Heavy cavalry were used primarily as shock cavalry; the intention was to slam into enemy formations and break them in melee combat. To do this, they usually had lances for the initial impact and hand weapons (swords, axes, maces, etc.) for when they were embroiled in close combat. As far as defensive accoutrements go, they typically wore the heaviest armour available, whether scale, chain, or plate, and - when they were still useful pieces of equipment - shields.

Light cavalry was used primarily for harassing enemies, raiding, skirmishing, and - most importantly - scouting and communications with the main force of their army. Their equipment was usually spears, bows, and swords. As far as armour was concerned, they didn't wear anything particularly heavy, as speed was of the essence.