The spin class bikes do use SPD pedals (and platform on the other side for those without cleats). You'll need an SPD pedal on the road bike for the same shoes to be compatible with both bikes. I spin and use Shimano PD-A530 pedals on my bike (one side is a platform). I never use the platform side and will, at some point, replace the pedals on my road bike. That said, the A530's are decent pedals for the money.