After placing either type of piston facing upwards with a redstone block directly above it, I placed a lever beside it and powered it. It extended, but now it appears that the redstone block is powering the piston, because deactivating the lever did not cause the piston to unextend. When the redstone block was broken, the piston did unextend. This only happens when the piston is facing upwards. Also, pistons are not supposed to take power from the piston side.