In my experience, no they are not the same heights. And you shouldn't bottom out the shaft in the collet to begin with, that can cause the bit to loosen as you run it. When you get the rail bit set how you want it, make some reference pieces from the same material. Then when you want to set the stile bit, use the reference pieces to set the height.
Make sure you run more material than you will ever need with the rail bit before changing bits, because it's a giant PITA to try to go back and set the rail bit exactly the same to run more material.
Ask me how I know.
Easiest solution is to set up on two router tables, one for the rail cuts the other for the stiles.
I'll burn that bridge when I come to it