There were 4 different versions of the movie in 2002 alone:
The digital cinema version that played in a hundred or so theaters in the U.S. had Anakin and Padme holding hands at the end whereas the 35mm version simply had Anakin’s metal hand hanging there in that shot.
The Imax version released later that year in November is about twenty minutes shorter since this was still the very earliest days of full-length Hollywood movies being released in 15/70 and the projector platters could only hold 120 minutes worth of film.
Apollo 13 was the first to get the Imax DMR treatment earlier that year and was also shortened. AotC was the second IIRC.
The platter problem was rectified soon after since the Matrix sequels released the very next year were not shortened for Imax.
The current limit is apparently 167 minutes, so there’s a reason the theatrical versions of Watchmen, Avatar, and the only version of Dark Knight Rises all happen to fit just within that running time. Interstellar just barely fit and apparently used a slide-show version of the end credits to shave off three minutes without removing anything from the actual movie.
Anyway, this brings us finally to the dvd/vhs version which was released within only a week or so of the Imax version (which never made any sense to me from a business perspective but then again this is the same Lucasfilm that decided to release TPM 3D in theaters several months after the blu-ray).
The main change made for the dvd/vhs (yes, they’re identical outside of obvious differences like framing) was the extended scene of Anakin’s confession to Padme about the Tusken slaughter. In the theatrical versions, it wipes to the next scene before Padme’s “to be flawed is to be human” (or whatever she says) and Anakin’s “I’m a Jedi, I know I’m better than this.” Btw, the audio of Anakin saying “I’m a Jedi” was used in that web-exclusive teaser-teaser trailer in October/November of ‘01, so it was a nice surprise when it showed up in the movie a year later.