I can go into more technical terms if you want since there are a lot more innovation in damage and armour in the past 3 decades.
To answer your question, I will answer in a general way.
In general, most games define critical damage as damage dealt by a critical strike (or critical hit). The probability of landing a critical hit is called critical chance. The critical damage is usually a percentage base on your character’s attack damage. For example, 15% chance of x2 is 15% chance to deal 200% of your attack damage.
This is to say that there are games that has other types of critical chance. Warcraft 3 for example has critical strike and bash (an also probability attack that does fixed bonus damage). Persona 3 for example introduces half-crit. Basically, the game runs two random event, one after another. If the first event is successful, it runs the second random event. Succeed in both events will make your character does a critical hit (x1.5 the attack damage). If only the first event is successful, you do a half-crit (x1.25 the attack damage).
In short, critical hit is just a probability passive to the character, introducing an extra random element to make the game more spicy by tapping into the gambling nature of humans.
Armour penetration or armour piercing or armour ignore is ignoring certain percentage of the target’s armour in calculating the damage receiving to the enemy.
If your character ignore 2 armour, then this means the damage calculation for that target will deduct two points of armour from the calculation. As someone else told you above, it also depends on how armour works in that game.
To be noted, armour penetration is only applied if the target has any armour. It does not reduces the armour to negative value.
Of course, there may be mechanic that affects the damage other than armour.
Overall, the chief difference between critical damage and armour piercing is one affects damage dealt while the other affects damage received.
Damage dealt is calculated before being plugged into the equation along with armour piercing to get damage received.