Well, fluorite is a manufuctured clay product, as opposed to actual sand. The "sand" version is just ground up finer.
Pool filter sand is a relatively precisely ground product, made from silica, very consistant, as it is designed to be filter media and trap specific particle sizes.
Play sand on the other hand is extremely unrefined, and can vary in its composition very widely. Nasty stuff, really...because of its inconsistent size it can compact and being messy, etc.
Blasting sand (black diamond, black beauty) is made from coal slag, but after its been rinsed is perfectly safe for aquarium use. It is manufactured specifically to run in sand blasting equipment, and so is similar to pool filter sand in terms of consitency. Great stuff for aquarium substrate. And cheap as dirt. (literally)