Most commercial printers print on paper. Seems simple and straightforward until one thinks about the different kinds of paper: coated and uncoated free sheet; coated and uncoated groundwood; newsprint. Even within each category there are gradations of quality, basis weight and brightness. It’s not so simple anymore.
Still sticking with offset, unusual but increasingly common substrates include folding carton and paperboard, card stock, plastic and lenticular. When there is a need for more specialized jobs, one normally thinks of flexo presses for flexible films and screen print for just about everything else.