First, let's define our terms, because the actual amount of armor and equipment carried by cavalry of any kind has varied enormously over the centuries, as have the definitions and terms applied to the horsemen.
I suggest that a better distinction than 'light' and 'heavy' cavalry would be Strategic and Battle cavalry.
Strategic is the cavalry that has the greatest effect Off The Battlefield - as in, those fast and nimble horsemen who can scout, raid, screen, harass the enemy's economy and workers and protect your own. They are usually not so good at fighting enemy troops in formation on the battlefield, because any heavy weapons (including heavy lances) and armor that would make them better at that would significantly degrade their ability to move far and fast and do the more important stuff. Yes, we can still call them 'Light Cavalry', but it has nothing at all to do directly with the weight of man, horse, and weapons in any Era.
Battle Cavalry, as the name suggests, is the horsemen reserved to fight the enemy troops on the battlefield. Since one of the cavalry's prime weapons is the mass and impact of the horse itself, these folks tend to charge the enemy a lot, and tend to be armed and armored so that they can get even more effect out of the weight and impact of their charge. So, in general, they tend to be heavier than the Strategic Cavalry, and also, in general, slower - both because of the weight carried by the individual horses, but also because the horses tend to be bigger, require more forage and fodder and feed, and therefore cannot just be 'turned loose' to range about the countryside like the Strategic Cavalry can.
The precise amount and type of armor worn by anybody is, in these definitions, not especially important. Yes, men who intended to charge in and fight the enemy face to face tended to wear more and heavier armor, but not always: nobody after the early 19th century wore any armor at all on the battlefield, yet the unarmored cavalry in virtually every army charged enemy troops in great masses - the British Heavy Brigade in the Crimea, Bulow's brigade and then division of cavalry in 1866 and 1870, and numerous regiments and brigades on both sides in the US Civil War.
In the Classical Era (roughly, 800 BCE to 500 CE) we are dealing with the first 'real' Cavalry - large groups of men on horses who intend to actually fight enemy troops in some way. They were learning as they went along, and one of the first things they learned is that it is much easier to use the horses' speed rather than their weight: keep out of the enemy's reach and throw things at him until he is worn down enough that you can finish him off with almost anything. Thus, the earliest riders are all shown using thrown javelins, spears, and bows - there are virtually no contemporary illustrations, and few accounts, of horsemen actually getting close to the enemy by choice.
So, as pointed out already, the few groups of horsemen who did actually 'charge' the enemy with Lethal Intent are all Specialists - dare I say, Unique. The Kataphractoi, a term first applied to Scythian (specifically, the Massagetai at Gaugamela, "armored horses and men from head to foot") Battle Cavalry, then to Sarmatians, both native and in Roman service (Equites Cataphractii Sarmatii) and then to horsemen in Persian and Byzantine armies. The other great Battle Cavalry of the Classical era were the Hetairoi - the Companion Cavalry of the Macedonians, used by both Alexander and his Successors and, although never as effective, copied by the armored Equestrian class cavalry of the Roman Legions.
That means, effectively, we can classify all the cavalry of the Classical Era as Strategic (Light) Cavalry with the only differentiation being the type of weapons they preferred. And those come down to two: composite bows (horse archers) and thrown javelins/light spears. And while numerous civilizations ranging from Persians to Thracians to Gauls, germans, Greeks, Romans, Numidians, etc all raised light cavalry with javelins, only the pastoral societies on the steppes raised horse archers in any numbers. If you wanted horse archers and were not a pastoral group, you hired them from the 'barbarians' - as did Alexander (4000 Scythian Cavalry in his army by the time he got to India), the Imperial Romans and the Byzantines (both of the latter had numerous units of Equites Sagitarii Hunii - hired Huns as horse archers)
But also note, if the distinction between Ranged and Melee is kept so that no unit with a Ranged Factor can attack an enemy unit directly, then the classical Light Cavalry should be Ranged horse archers and Melee Light Cavalry. IF Civ VII does away with that rigid distinction, then the classical Light Cavalry would be cavalry which can either make a ranged or melee attack - but not both, because it took a certain amount of prior planning to keep a javelin as a thrusting weapon to close with the enemy and not throw them all and then ride away before the enemy can catch you, which seems to have been the cavalry's preferred method of 'fighting'!
