As others have noted, it was re-coded.
The primary difference is the removal of slowdown. The original Sega CD version suffered from tremendous slowdown that occurs in every single level in the game. It's really quite shocking how often the framerate dips on Sega CD. It's nowhere near as smooth as the Genesis games.
In addition, the special stages ran at like 20 fps on Sega CD while they operate at 60 fps in the updated port.
That's really the main issue right there. You get other improvements with the update version as well but the smooth performance is what makes it vastly superior.
This thread made me pull out the Steam version, which I bought on the last amazon sale, but I have never actually played yet. I bought the iPhone version way back when it was released and played through and completed that one, and played through it again after the first patch was released that fixed a few issues. But the Steam version has been in my backlog for a while now.
But playing through the Steam build... wow. 75FPS at 1900x1200 resolution. It is so smooth, and no flicker or slowdown ever. It's a real treat playing a 2D platformer like this and something that I don't see very often. The Sega CD version definitely had slowdown and flicker in comparison, I think it was a latency issue between the Sega CD and Genesis that caused a lot of that.
I also pulled out my Sega CD version and ran it in Fusion for comparison...
Sega CD version running on Kega Fusion (ignore the 960x720 resolution and the SuperHQ Sound Disabled message. F11 is is my fraps screenshot key, which is also shared by the HQ sound key)
HD Version:
Aside from the 16:10 aspect ration (that's how my monitor is), you can already see some pretty noticeable differences. More of the playing field is visible, and also that spinning ring clearly has more frames of animation present in the HD version (which you can't see). It animates much smoother.
Another difference here is that the Genesis game uses fake transparencies (basically just the checkered solid/ blank colours) which is typical for Genesis/ Sega CD games...
HD version uses real transparencies.
Bonus Stages are much higher resolution in the HD version, obviously. But as pointed out before they run at 60FPS (well 75FPS for me) here while the Sega CD original had the playing field run at about 20FPS with the BG layer running at 60FPS. Sprite scaling on the UFO's are much smoother too.
In the Sega CD game, the spindash uses Sonic's standard roll animation, it doesn't animate differently:
In the HD version, he uses the Sonic 2 spin dash animation. Also the spindash works differently, here you have to charge it up by tapping the action button. In the original the spin dash is charged by holding it down for a longer period of time. Original and Sonic 2 mode can be switched in the options menu:
In the Sega CD game in Tidal Tempest, the sprites for the top of the water flicker really fast off and on. This is to try and simulate some sort of transparency effect. All the Genesis Sonic games did this.
In the HD update, the top of the water is actually transparent this time and does not flicker. Also, the background layer and playing field layer both have a swaying effect applied to them. In the Sega CD game, it's just the BG layer that sways.
There's a lot of little changes all over the place visually. Too many to list. And as pointed out by Dark10x the music is actually extended for some tracks and does a proper loop. While the Sega CD version usually fades out at the end of the CD tracks and just restarts at the beginning. The transitioning sounds so much nicer in the HD version audio.
There are a few inaccuracies, though... IIRC you can't activate time travel using the vertical conveyor belts in Quartz Quadrant, like you could in the original. This was fixed in the mobile versions, but thanks to Microsoft's draconian XBLA patching policies, I'm not sure the console/Steam versions will ever get fixed.
I don't know really if the Steam version was patched to fix some of those issues. I will have to play it through to find out.