Hi everyone !
When you finish the story in normal and ultimate vault hunter mode, and get the level 50, you will start to farm legendary weapons, BUT there is a type of weapons “better than legendary weapons”.
I wall them vault weapons, some guns have is Antoined version, vault weapons are better than normal weapons.
For exemple :
The Butcher
The Antoined Butcher :
As you can see, the Antoined have a better stats than the normal butcher.
How to reconize Antoined weapons ? Thats simple Antoined weapons have a vault logo on the top of the guns description, and they have a bonus skill :
Also when a Antoined weapon drop, there is a bigger light than normal weapon :
(At the left normal weapon, at the right vault weapons)
Antoined weapons also give you some bonus capacity (like on the butcher) !
It’s long to farm Antoined weapons, they have a very little chance of drop, to farm it fast, be sure have chance bonus stats, and play in ultimate vault hunter mayhem 3.
The most common Antoined weapon ( i have drop it like 3/4 time more than other weapons) is the Hellwalker ( i call them doom shotgun, because it look like doom, it sound like doom, and there is an electric guitar sound when you shot with him.)
He drop more than the other Antoined weapons 
Antoined is not only for weapons, you have Antoined shields and Antoined grenades to !
I hope this topic will help you to understand that types of weapons !
And i’m sorry for my english, i have some difficulties in this language .
Have a nice day !