Case #1: The Title Screen

The most obvious difference is the fact that Sonic CD is spelt "CD Sonic" other differences include:
-Different Dr Eggman picture in the mountain.
-Non-3D clouds.
-Different looking Little Planet.
-Sonic looks slightly different.
-No Trademark sign.
-Option are in the middle of the screen rather than the bottom.

Case #2: Time Attack

The exit graphic is different.

Case #3: Special Stage

You only get one special stage, and it is a demo. Note the funny remark ^_^

Case #4: The Sign Post

Sonic's spines are in a different position and his facial expression is slightly changed.

Case #5: Amy Rose

Amy's face looks different from the final.

Case #6: Monitors

These monitors don't appear in the final Sonic CD levels unless you use debug mode. The blue ring gives you invincibility and speed, so do the "S" monitors. The Clock monitors freezes the rings temporarily. Other sources claimed that the monitors turned the blue rings into life monitors. These monitors were most likely taken out of the game because they had no real valid use for them.