Sonic 1 US was the first release of the game in June. The Japanese game came out in July, and Sonic Team was able to tweak it a little. The big differences in JP Sonic are extra scrolling effects in most of the Zones.
Green Hill has scrolling clouds that move against Sonic on their own
Marble has scrolling backgrounds(the ruins and grass move with Sonic) and clouds that move with Sonic
Spring Yard has the same things
Labyrinth has rippling water effects
Starlight is unchanged
Scrap Brain has clouds that scroll with Sonic
I don't know if there's a second JP Sonic 1, Sega had an ad that named the game SegaSonic the Hedgehog but I don't think the name changed on the product itself.
~ SA Tails