Damage N means to deal N Damage to a Unit. This may be done directly on a TARGET, or indirectly through an Effect. Damage N is most commonly done through Attacks.
The Effect Syntax is:
Damage N Unit
X Damage means to modify the Damage whenever a Damage N effect is done. This happens most frequently during the second step of the Attack Calculation.
A Damage N Effect creates an X Life Effect.
When we refer to "damage", we mean the Damage N Effect.