Emma Stone was 23 when The Amazing Spider-Man came out in 2012, and she was 25 when she returned for The Amazing Spider-Man 2 in 2014. Her birth date is November 6, 1988, so she was in her early 20s during the Spider-Man films.
In the first movie, she played Gwen Stacy, a high school student, so the age gap between actor and character was fairly typical for a teen role in a major studio film. Reports about her being 22 or 23 during production can both make sense, depending on whether the reference point is casting, filming, or release.
The simplest answer is: Emma Stone was 23 in the first Spider-Man movie and 25 in the sequel.