affixes would be Normal (Yellow - max 5 per item), Epic (Orange - max 6 per item), Legend (Red - max 6 per item), and Crystal (Light Blue - 1 per item, excluding Pets). I guess you could consider these regular affixes.
other affixes would be Set (Green - 1 per item. can be found on Legend Pets also). Set affixes go from rank (1) to (8). Set Bonus (Grey?) can be found on certain items, and need a certain number of Sets or conditions to be activated. Seven Deadly Sin items also have a Set Penalty (Pink?) in addition to a Set Bonus. if you have enough of the 7DS Set affixes, you can activate the Bonus’s to overcome the Penalties.
Myth Stones (Purple - max 6 per item, excluding Pets) are a special affix with about the same power of either Normal or Epic affixes, with a few about the same power of Legend affixes.
Mythic Affix (PURPLE - 1 per item, excluding Pets) these require a recipe of 4 Myth Stones to create. they only go on certain items, except for Resource Mythics, which can go on any non Pet item.
because there are only 36 spaces for affixes, 42 if you have a Pet, you end up finding ways to make affix combinations to do a lot of damage while keeping you alive. not only that, some Weapon Skills and Class Talents work better with certain affixes than with others in certain combinations. a good example would be having an OH with Smoke Bomb Skill, 2x Smoke Bomb Proc, Smoke Screen (5) Set, Smoke Bomb Skill 40, and the Noxious, Darkness & Bombardier Talents at 40, with a few extra AoE affixes to increase the size of Smoke Bomb. this would make a good foundation for a Smoke Bomb build for Rogues. Mirrorcast (Legend), Elemental (5) (Green Set), and Specialist (Legend) would help cast even more Smoke Bombs. and you still have space for other affixes to improve damage or defense.
I know this is a lot, but I hope it helps.