From reading the rules it would appear there are two kinds of damage and then straight loss of life:
118.3 If an effect causes a player to gain or lose life, that player's life total is adjusted accordingly.
From reading that I would guess that effects like Extort are not sources of damage. You simply lose the life.
119.2a Damage may be dealt as a result of combat. Each attacking and blocking creature deals combat damage equal to its power during the combat damage step.
So damage from creatures during combat is combat damage.
119.2b Damage may be dealt as an effect of a spell or ability. The spell or ability will specify which object deals that damage.
And that is direct damage from an object.
So the arguments are these:
Does loss of life as outlined by rule 118.3 (at top) count as being dealt damage? Do triggered abilities that redirect or reduce damage effect loss of life?
My second related question: You put Arcane teachings on a Blinding Angel and tap her to deal one damage to your opponent. Am I right in saying that because the damage was direct damage (not dealt during combat) then the triggered ability of preventing the combat phase of the damaged player is not triggered?