I think your looking at a couple of different processes all at once here.
Sublimation process – uses a chemical reaction to dye the special coated object or polyester based t-shirt. Using special inks (sublimation inks) you print onto dye-sub transfer paper, this is then placed onto you object / t-shirt, pressed with heat to turn the dye into gas which then transfers & dyes your printable object.
Transfer Paper Process – eg Magictouch. The transfer paper is a special media that is general used with laser type printers. The image is printed onto the transfer paper to basically make a decal type sticker (Not totally accurate, but easiest why to describe it!), again using heat the decal is bonded onto the t-shirt, BUT it does not ‘dye’ the t-shirt, its a sticker, this is why you have to cut around the graphic before transferring or you might see the transfer paper.
Does allow to print onto cotton & dark material unlike sublimation.
Hope that helps?