Yes, there are pretty significant differences. You want to spend as much time in the saddle of your race bike as you can -- even if that means it is parked in the training. Riding your race bike in the trainer will allow you to adjust to the seat, hold race position, gain or maintain flexibility in the aero position, get more comfortable on your bike, and prepare for being able to hit the road. Spin bikes have their place -- don't get me wrong -- their place is for spinning classes to break up the monotony of indoor riding. However, you cannot replicate the feel of the road bike on the trainer by using a spin bike.
The one exception may be the Cyclops stationary bike w/ the built-in power meter (cannot remember the name). It is highly adjustible and gives you the ability to monitor power. However, no matter how close you get, it is not your race bike.
If there are no dogs in Heaven, then when I die I want to go where they went. - Will Rogers
Emery's Third Coast Triathlon | Tri Wisconsin Triathlon Team | Push Endurance | GLWR