Same character, different NPC, if that makes sense.
The first Abnur in the armor is the quest giver for The Demon Weapon, which is a prologue to the Elsweyr DLC. The second in the guild robes is the quest npc variant who appears during The Tharn Speaks as part of the main quest.
ESO's game design wants all content to be available to start to all players immediately regardless of chronology, and puts the quest givers for DLC content in starting areas. This makes it really confusing for new players trying to follow the main quest since some of the quest givers are characters that are also tied to the main quest, like Abnur and Lyris.
Pact players get it the most confusing, since Abnur 2 was carelessly placed inside a building he already appears in - and is supposed to be talked to in - during the main quest for that alliance. For DC and AD he is located in the local government buildings (castle/manor house, respectively) but I guess since Davon's Watch doesn't have any sort of castle or manor they went with the Mages Guild, not realizing how weird it'd be.
Basically, talk to the first guy if you want to do a quest setting up the story of the Elsweyr chapter and leading you into playing it, and talk to the second guy if you want to keep along the main quest for now.