Choosing shell back vs solid back can affect the look of the back of the badge as well as the weight of them. Solid back badges are a bit heavier than shell back badges.
Either option can be glued into a wallet without any issue. In the case of glueing it into a case, the badge back choice can mostly be a personal preference.
Shell Back Badges - ridges & indentations similar to the front of the badge.
Solid Back Badges - Smooth on the back.