By the power of truth, I, while living, have conquered the universe.
The Forerunners didn't go extinct, they left the Orion Arm of the Milky Way after they reseeded the galaxy of life because they failed to uphold the Mantle, so they passed it down to humanity (as the Librarian saw us as special) which made humans Reclaimers and gave us access to their technology and allowing us to activate the Halos.
343 GS was mad, he would not have been allowed to know every part of the Forerunners' plan, as he states that his knowledge was strictly limited to his programming duties on installation 04. He identifies Reclaimers to be the same as Forerunners, which is wrong.
Humans were discovered by the Forerunners, they are 2 very different races. It's speculated that humans are actually de-evolved Precurosrs, but that's too much of a grey area to elaborate on.
The aesthetic look of the Forerunners in Origins is COrtana's interpretation on what the Forerunners would look like from the information she's gathered; it is not neccessarily accurate.