The core plug (see attached pic) is a piece of black plastic that goes into the cardboard core of the roll. It has a 1" diameter hole in the middle for using with our dispenser, or any 1" dowel/rod/etc. This makes it roll easily for dispensing.
The pad plugs (in pic of original thread here - the 2 white pieces at the ends of the box) are used for holding a roll suspended in a box so that it dispenses easily from the box itself. Foil rolls typically have pad plugs in the box.
Hope that answers it?