My front tire has the skinny valve (I believe it is a Presta) and so does my rear tire. But my rear tire also has a screw-on piece that goes over the valve which I believe to be an adapter. Do they simply provide one adapter because it is cheaper and you can move it from one tire to the other?
The adapter is only meant to be used while pumping up the tire. You shouldn't keep it installed while riding.
Many bicycle pumps can be used with both presta and shrader valves, but I'd reccomend that you keep a pump around that can pump presta natively so that you never need to mess with the valve adapter.