Iirc, from some stream or another conversation from long ago, the AI director (in addition to the other things mentioned) gets Special spawns quite regularly, but often “saves” them to release a bunch at once. After that, it may bring up a couple of others to replace the killed ones (there’re clear maximums for simultaneous specials, depending on difficulty), but after that it’s more likely to start “saving up” the spawns again.
This does cause the Specials to generally spawn in short sprees, often two of one type and a couple of others (on Legend; on Cata the limits are obviously bigger) at once. As for Hordes, they’re on a timer but it’s partially random and doesn’t line up with the Special spawns; there are also two types of hordes (“normal” and ambush) with different compositions and timings. Monsters and Patrols are on triggers from moving in the map, and thus are directly irrelevant to other threats (though hordes are limited during Bosses, mostly to give time to kite and clutch). Elites are mostly just the “roaming” enemies that populate the map independently of anything that spawns during the run; hordes gather them from the surroundings to assault you with them, but once you’ve slain them, they’re gone (though Cata’s different on that account).
All of this makes for pretty varied encounters, and when a Boss trigger, either kind of horde and a bunch of Specials line up it’s a pretty significant spike in difficulty.