EDIT: I've found the answers and I've decided to publish them here for everyone who's curious of it:
1. Aura HD has built-in app store (not iOS ;) ) and is produced with intention to be network media players, not "only STBs". MAGs are "only STBs" with services as an add-on. These intention is to be used by IPTV / OTT operators who would want to integrate it with their middleware and their features (e.g. Ministra).
2. Aura HD / Aura HD International = MAG 250
Aura HD Plus / Aura HD International 2nd Edition = MAG 254 / 255
Aura HD Pro = MAG 322
Aura HD Plus T2 = MAG 275 / 276 (276 is closed version).
3. Probably it's the same firmware, I'm not sure. In the description for software for MAG 322 there's also Aura HD Pro written and I've found that the latest software for Aura HD Plus is "0.2.18-r22-255" (255 = MAG 255) and the same of "original" Aura HD (0.2.18-r22-250) and Aura HD Plus T2 (0.2.18-r22-276).