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Out-of-universe; Although the soundtracks were different in the original versions of the game (Japanese and US), there is something to be taken with the US soundtrack. The Past tracks, which are shared, represent what was originally going to be in every version of the game. The Present represents what changed through No Export for You-esque circumstances, and the Futures represent that the changes were persistent and will evolve, as the Sonic Gems Collection shows. (Not implying that Gems changed the music. Just noting that it has a version of Sonic CD on it. And it was released after Sonic CD, therefore, the future.)—Akamia
Better than that. It also hints that somewhere along the way, there was a Split Timeline event, which after the Past, changed the music for the Present and Future.
The Japanese boss theme samples "Work That Sucker To Death". In Quartz Quadrant, you defeat Eggman's conveyor belt contraption by running the belt until the console platform Eggman is standing on wears thin and he's forced to flee. In other words, you literally work that sucker to death.
In regards to the music, both Ogata and Nilsen were in the right mindset for the musical theming of the zones.
Palmtree Panic's tropical feel: In Japan, the closest to the tropics that Japan can get is Okinawa, which explains why in America the music now sounds like it's from the Caribbean.
Collision Chaos: Both have an urban feel to them but implemented differently. Japan does it like it's Akihabara, while America does it like it's either Chicago or New York.
Tidal Tempest's watery feel to it is implemented a bit differently in both regions. In Japan it has the ocean waves and a ancient feel to it while America uses the ancient feel for the Bad Future, but it still has the watery feel to it with the slap bass sounding like drops of water.
Quartz Quadrant has a sort of rocky feel to it. This is apparent in the Japanese version, while America took rock as rock and roll.
Wacky Workbench has an industrial feel. In Japan, this is heavily reflected in the bad future with the warning siren going off, while America has it sound like a building is being put up.
Stardust Speedway is a bit interesting as Japan does it like a bright night on the road, while America has it sound like Sonic is on a racetrack, and adds a bit of foreshadowing to his eventual race with Metal Sonic.
Metal Madness both involve a techno/rock feel to them. In Japan, it includes the late Casey Rankin chewing out Eggman in rap form that all of his plans have failed and his ultimate weapon has fallen. America meanwhile is heavy on the techno in the Present and Good Future, while heavy on the rock in the Bad Future, showing that Eggman is starting to descend into insanity.