Big Four

These are four very common distinctions made in rule text which new and old players may not realize.

Basic attack/Nonbasic attack
Attacks are classified as two different types. To quote the nonbasic attack article:

This is a common answer to questions like "why didn't (attack) trigger (passive ability)" -- the attack was a nonbasic attack, and the passive ability only trigger on basic attacks.

Successful Attack Required/Damage required
Sometimes effects will trigger even if the attack hits but does no damage -- different abilities require different things. Check the rule text to see what is required. If it states "If successful..." or "When this champion makes a successful attack...", then the attack will trigger even if the damage is redirected or prevented (as long as the attack doesn't miss).

Damage/ Loss of Life
There are two ways to reduce a champion's HP. The most common way is for the champion to take damage, but a champion can lose HP directly -- this is sometimes called "Loss of Life". Some effects (especially Impervious) reduce damage, however these damage-reducing effects are ignored when a rune/ability states a champion "loses __ HP" or "loses __ life". In other words, "loss of life is not damage".

For example, a champion which is Impervious won't take damage, but it can still lose HP from Hex, Drive, Death Pact, and so on.

Attack/ Damage Ability
Some abilities (such as Pounce) allow a champion to deal damage without attacking. These abilities may or may not be on the attack chain (see this page for some examples).

Since these abilities aren't attacks, an opposing champion can't avoid them using Deflect or Dodge. Champions who are Pacified are usually still able to use these damage abilities.