Why don't most non-East Asian varieties of rice stick together?

Having tried a number of different kinds of rice, I've noticed that the only ones that seem to have grains that "stick" together are white varieties often used in East Asian cooking (jasmine (to some extent), Calrose and other "Japanese" types, etc.). (Glutinous rice also has this property, albeit to a much more pronounced extent, for obvious reasons.)

Conversely, a lot of other types don't (at least not to the same extent, and when they're not overcooked). For instance, the rice often served at Middle Eastern restaurants doesn't "stick". Nor do basmati or red/brown varieties. I've also had mixed experiences with white rice of the American long-grain variety, although there's the possibility that the place that was serving me it was undercooking it.

For what it counts, the only types of rice I've had experience cooking with (either stove-top or in a rice-cooker) are jasmine, Calrose, and red and brown varieties. I rinse my rice, but would not know if the rice I've had in restaurants or other types of eateries has been, and I'm not sure if this might result in a difference.

Thus: why is there such a difference in "stickiness"?