While in theory there might be a difference in force delivered from "heavy" cavalry to light cavalry due to the difference in mass in horse, armour and weapon, here we are talking about the difference of being hit by a minivan or by an SUV. The classification of different types of cavalry has (fairly) little to do with what happens when they hit an enemy line and far more with what they wear, on what horses they sit and how they are used on and outside the battlefield.

In some sense classifications like light, shock, heavy, super heavy are artificial and made for the modern men to have a category to sort certain units from certain times into. However we do have some historical references to some classifications, for example in the Napoleonic army. Classifications like these however vary from time period and era to the next. What a late medieval European man-at-arms would call "heavy cavalry" might be very different from what a Roman or a Napoleonic officer would call heavy cavalry.

The most tangible to classify cavalry (and infantry for that matter) in concepts like light and heavy is to look at how they are used and how they equipped in relation to other comparable forces from the same area at the same time.

Light cavalry is generally speaking not expected to engage in direct hand-to-hand combat with infantry units or do much fighting at all.

Hussars were true light cavalry, used best for raiding and scouting. They rode smaller horses, carried somewhat lighter weapons and curved sabers, and wore costumes typical of their origins.

John A. Lynn - Giant of the Grand Siecle_ The French Army, 1610-1715 (1997) p.492

These units were arguably even more important outside of the battlefield, where they were provided intel on the enemy forces and the territory. On the battlefield itself they are mostly skirmishers, give chase to fleeing units and screen troops. While in theory an attack by light cavalry might be just as deadly as from heavy cavalry, this is where the term "light" matters since it refers to the level of armour. For these forces, closing in into missile fire, be it archers, slingers or javelins would be devastating. They don't have the level of armour that allows them do approach a unit that is covered by missile fire without taking heavy losses and as soon as they engage the enemy they are still very squishy targets in hand-to-hand combat.

My personal standard for heavy cavalry, pre-black powder, is that they comparatively unlikely to get injured at range by arrow fire. While light infantry in all eras looked kinda similar, heavy cavalry changed a lot. We have the Cataphract, Aswaran and norman knights who would all count as as "heavy cavalry" but still are not in the same league as a late medieval men-at-arms in full plate.

In regards of the Aswaran:

This may suggest that armor had become so highly developed that the super-heavy Savaran did not consider Roman archery as a threat. The range of weapons increased to include weapons such as axes, maces, and darts.

By the time of Julian’s invasion of Persia in AD 362, super-heavy Savaran knights are described as being consistently covered by mail, and subsequently being “lifted up [onto the saddle] by others because of his weight” (Heliodorus, IX, 14, 5). Weight of armor did not pose a problem once the warrior was on horseback

Kaveh Farrokh, Angus McBride - Sassanian Elite Cavalry AD 224-642 (2005, Osprey Publishing) p. 17; 28

With the Savaran/Aswaran they are not only heavy cavalry (some would call it super heavy which I find questionable) but they are also horse archers. This might be compared to the Japanese Samurai. This of course does not work as soon as full plate armour becomes the standard in central Europe but was a rare concept there anyway. It did however gain momentum when black powder found it's way on the European battlefield.

This heavy cavalry would also be the cavalry which has at least the ability to strike into a formation though even that is rare since horses generally speaking don't want to charge directly into a wall of humans. The ability of actually reaching the enemy formation however is what makes this cavalry into "shock" cavalry however the intention is not as much to actually have the horses collide with the enemy force but to have them run away. Which, if a group of almost 1 tone horse, potentially clad in armour, with a guy who is fully in armour and a lance sticking out is a fairly reasonable thing to do. The shock and terror doesn't come from the impact but from what you see charging at you.

Depending on what area and time period we are talking, we might also see different horse breeds being used for different tasks. Heavy cavalry in the late middle ages for example would use a horse which would be closer to a modern draft horse while skirmishing units and light cavalry could be seen on everything from almost ponies to medium-sized horses.