Printing on fabric would generally be referred to as "Direct-on-Garment" or DOG printing and is a common method for making small-run clothing items like custom

Printing on fabric would generally be referred to as "Direct-on-Garment" or DOG printing and is a common method for making small-run clothing items like custom T-shirts a la CafePress. The quality is generally (but not very noticeably these days) worse than screen printing but there are no setup costs involved. The main issue with DOG printing is that poor adjustment of the heads can result in some overspray (as they must sit some small distance from the fabric to avoid smearing). This can be avoided by competent operators, the big internet companies just don't always bother.