Elixir Field misnamed.

[CosmicKirby]

Monks are the only DPS class that has it's own Heal ability (disregarding the life steal that DRGs have). Monks have the ability to heal, because of their real life lore. They are able to harness their own Chi to recover.

While i agree that Elixir Field makes sense in the justification of MNK, you're kind of wrong on this account.
PGL is the one that earns Second Wind. A term very often used by athletes, runners, boxers (in particular) etc. to refer to a burst of energy after one has initially hit 'the wall' of exhaustion where they feel they can't push on. After enduring through the wall, they usually find a resurgence of breath/energy and continue to push further. Given the class, and possibly the localization, there's nothing mystical about Second Wind at all, it's just a result of the PGL's fisticuff training.

[Thunda_Cat_SMASH]

You can say that, but if you look at the animation, the character definitely strikes a very martial arts pose with a small stamp. There's also the fact that during the animation you can clearly see energy being drawn into the pc through the atmosphere, so it's possibly a result of martial arts training.