It depens on the region you are looking at. In South Eastern Europe you would have the Cataphracts of Byzantine/Arminian tradition which were extreme heavy cavalry that could steam roles enemy infantry or cavalry. Yet through the heavy armour of horse and rider, thier maneuverability was lesser to the light cavalery that they faced. Light cavalry could flee from its charge and flank it. Or more common led the Cataphracts follow them in an ambush position. Same is true for horse archer, that like most of the light cavelry come from the Central Asian steppe nomad tradition, which would additionaly pepper the heavy cavalry with arrows. Although the composit bows might strong, yet even the stronger long bow, contrary to populair belief, would have issues in perfect situations to penetrate steel armor. The hail of arrows woul pick off light cavalry but irritate and stress heavy cavalry, with from time to time hitting a weak spot or gap in the armour and wounding or killing the rider. The heavy cavalry would accompied with light cavalry that would function as scout an pick of light cavalry or skirmishers.

In Eastern Europe you would have normally light cavalry, which would fight each other or dismount and fight on foot as mounted infantry. This was often quick and maneuverable, often the engagement were nothing more that skirmishes.

In Western, Central and Southern Europe, were you possible aimed your question at. Cavalry combat took place between heavy armoured knights and lesser armoured men at arms when they were mounted. In cavalry engagement was in a battle main statage and decided the battle. The riders on both sides would charge with lances, aimaing to displace the enemy from the settle. after the first clash lance would be disgarded. combat continue with sword and mace. The aim in combat is not to kill the enemy but to make it impossible to continue the fight, most important reason not to kill was to make prisoners which could be exchanged for money. the combat would continue till on side is pushed back or lose moral and breaks. often fighting would be mixed with fight of the infantry or knights whose horse were killed and continued to fight on foot. Maneuverablility and control once the charge was on it way was low. through difficult of commucation on the battlefield and overal chaos, only pre-battle planned easy maneuvers were excuted, and often poorly. As active inteverance of the comander was often difficult and often was he in mids of the battle and himself often lost overside.