As you alluded to in the last paragraph, Harry just went through an incredibly traumatic series of experiences (Third task + portkeying to graveyard + Cedric's death + Voldemort's return + Duel with Voldemort + Crucio + Priori incantato + Finding out Moody was Crouch).
It's entirely plausible that he may not be up to faithfully memorizing 100% of what was said around him to other people, especially a random name.
However, just to be clear, it was clearly and certainly the same Mrs. Figg:
Question: Is the Mrs. Figg with all the cats in the Dursleys' neighborhood the same Arabella Figg that Dumbledore mentioned at the end of book 4?
J.K. Rowling responds: Well spotted!
(src: "About the Books: transcript of J.K. Rowling's live interview on Scholastic.com," Scholastic.com, 16 October 2000)