That is an open and unsolved discussion (no hard science at this time). But many of us feel there are differences in flywheel speed/mass/angular velocity and the effect on the body.
There may be functional differences that load the body differently and could affect the results of an FTP test and subsequent training.
I feel there is a real difference and that testing and training should be conducted in the same basic conditions in most cases. I do advocate mixing the flywheel speed in training and that mix should vary based on rider and event needs.
Here is a thread with lots of related discussion.
All that said, it makes sense to me to test the same way you do most of your training, on the spin bike. Even beyond those potential differences, there are likely other environmental changes that may impact you as well (temp, fans, etc.)