Buzz Lightyear-Portrait

They never really gave a reason for why Buzz Lightyear believed he was a real person instead of a toy, none of the other toys we meet before or after ever seemed to have that issue. Woody didn't even know he was part of a very old and popular franchise before the 2nd film.

Personally, my head canon is that because Buzz was conceived of with such an elaborate backstory and clearly defined persona, this somehow influenced whatever mysterious force it is that gives toys a life of their own. Most of the other toys we see are basically blank slates for kids to play with however they want, but Buzz was definitively a space action hero, and that's how you were supposed to play with him.

Anyway, in my personal opinion, the character of Buzz Lightyear was better realized in the spin-off cartoon, Buzz Lightyear of Star Command. Of course, I may just be biased since it was a sci-fi action show at a time there weren't many on TV.