A die cut refers to a sticker being cut directly from the sheet. So, if you were to order die cut circle stickers, you would receive a perfectly round sticker.
A kiss/contour cut refers to leaving the sticker on the sheet. If you were to order kiss cut circles, you would receive a square piece of vinyl the circle sticker can be peeled off of. This option is great if you want to your sticker to have a display around it.