cupcake/muffin paper liner confusion

This might seem like a really dumb question, but it's one that's been bothering me for awhile. When you make cupcakes or muffins in a muffin pan, are you supposed to use the paper or the foil part of the disposable liners? I've always used just the paper part, but the other day I bought a new box of them, and noticed the instructions were to use the foil liners and discard the paper ones (it also recommended just using them on a sheet pan rather than using muffin pans).

Wouldn't the foil ones within a muffin pan cause the cupcakes or muffins to bake differently?