does it moves up and down with the valve stem??
Poppet valve is the commonly used term for a standard, mushroom- shaped engine valve.Obviously, the mushroom head is part of the valve, so yes, it does move up and down with its stem.
A poppet valve is a valve consisting of a hole, usually round or oval, and a tapered plug, usually a disk shape on the end of a shaft also called a valve stem. The shaft guides the plug portion by sliding through a valve.. not sure if you are talking about tire valve stems? if so the poppet valve moves within the valve stem. I have also heard them referred to as Schrader valves see link