The difference between glutinous and non-glutinous rice is essentially chemical in nature. The relevance of this difference to cooking recipes is one of texture: since the rice types have different properties when cooked, they add different textures to recipes. When combined, they add a third possible texture. Non-glutinous rice became more popular than glutinous rice during the 1940s through 1970s during what is called the Green Revolution, which is when farming technology transfer initiatives to benefit Asian countries occurred.
Historically, glutinous rice, also called sticky rice because it sticks to itself when prepared correctly, was the common rice of Asian countries. Farmers had agriculturally selected the sticky varieties that narrowed down to one single genetic variant and monopolized rice cultivation for 2,000 years. Incidentally, Laotian farmers never switched their preference to non-glutinous rice varieties.
Glutinous rice does not contain gluten and so is classified as gluten-free. In reference to these rice varieties, glutinous means glue-like, hence, sticky rice (with no reference to gluten content). The sticky quality comes from the rice's chemical composition, that being the absence of amylose and a high concentration of amylopectin, two starch components. In addition, as Kasma Loha-unchit explains, when uncooked, glutinous rice is opaque (not transparent) whereas non-glutinous rice is transparent, but, when cooked, glutinous sticky rice becomes translucent while non-glutinous rice becomes opaque. The difference in price is negligible. The difference in texture and sticky-action is significant.