As far as I understand you can perform tier throws, combos and simple melees. I think there are ki based tier attacks as well but this hasn't been expounded on. Not sure how the grab and drag will look like, maybe it'll look like the sliding effect seen in the New Years 2013 trailer......the final melee guide video has a grab and drag but it probably looks much different now.
The Tier attacks are special moves you can do by acquiring enough bonus points, and then spending them. They are big damage attacks, that go though blocks, and win any head on collisions as long as the opponent is not using the same or a stronger tier than you.
They are NOT separate for the 3 melee types. So using ANY kind of melee when in "special" mode will result in the selected tier being used. You select a tier by either pressing the bonus button once, twice or 3 times respectively for tier 1, tier 2 or tier 3.
The higher the tier the stronger the attack, the more bonus points it costs, and the shorter the time period you can use it in, before you just waste bonus points without landing an attack.