the Green border Items are Eternal Tier Items. they can only be found as Treasure. I’m not sure, but I think that there is a 1% chance for any Legend Item to be found as an Eternal Item instead. when you buy Items in the Shop, if they are Legend, there is a 1% chance they may be Eternal. Treasured Perk and Eternalized Set can improve the chances of a Legend Item becoming Eternal.
the Cyan (Light Blue) border Items are Crystal Items. Crystal Items have one Crystal affix on them. Mythic and Eternal Items with a Crystal affix will have their Purple/Green border. I think that there is a 1% chance of a Legend or Eternal Item having a Crystal affix. Treasured Perk and Crystalline Set can improve the chances of their being a Crystal affix. you can use an Obsidian Crystal to put a Crystal affix on any Item expect for Eternal Items. Legend and Eternal Items can only have a Crystal affix if they have an affix that is on the Crystal Affix List. 
here is a Post showing which Crystals can be used on Eternal Items…
and here is a Post for restricted affixes when using Amethyst and Ruby.
hope this helps.