The difference between the two modes is that one is free for all, and one is just for the last 3 years or cards + leaders - Ambre.
Within each of the modes there's three different levels, one for 23* and under, second for 32* and above, and third for everything in-between. So if you use a low star deck in a dt, you don't get paired with a 40* deck, and vice versa.
Instead of T1 and T2 they put all the players in the same room (Extended or Standard) but only allow your decks to challange players in your * level.
Level 1: 0 to 23 stars
Level 2: 24 to 31 stars
Level 3: 32* stars+