Fantasy events may be chosen; otherwise they're off by default. Fantasy events are mostly a set of Byzantine revival and independent Wales events and won't affect the vast majority of games unless you're playing one of these countries.
Random events can be turned off (default on). These are the events such as "exceptional year" or "new vein discovered" that pop up every 10-15 months for each country (in later patches; only the 'playable' countries in early patches). The game engine requires random events; AGCEEP got around this by putting in a few events that have no effect. If you turn off random events you're really just turning off the effects, not the pop-ups.
The two are completely independent of each other. You can have random events but not fantasy events or vice versa.
As a side note, all of this applies only to the AGCEEP.