The difference between kiss-cut and die-cut
As described above, there are two ways to cut out stickers.
The stickers are cut onto a sheet, leaving the backing (the sheet they are cut on) intact. You only remove the stickers from the paper. This is called a kiss cut: only the sticker is cut, not the backing.
Sticker cut with a kiss-cut
The backing of the stickers is still intact. The stickers are cut loose on the pages.
The second method involves fully cut stickers that are no longer connected to each other. Both the sticker and the backing are cut. This is known as a die cut.
Stickers cut with a die-cut
Both the sticker and the backing are cut in the round shape of the sticker.