The Tetori is an archetype for the original monk and uses all of its stats and features that are not modified by the archetype.
Unchained monk archetypes, of which are are a few, should indicate somewhere on the page that they are for the unchained monk.
As for what the unchained monk is, I'd say that it's an attempt to make a class that more closely and effectively accomplishes what people think the monk should do: a hand to hand combat expert with some mystical powers. I'll leave it to others to say whether it's balanced, but it's definitely stronger than a core monk that doesn't take any archetypes.
