On the post about non-Vancian non-spell-point magic systems, faoladh objected that a fatigue system is really a spell-point system. But the truth is: they are all spell point systems. Using scrolls as your primary means of casting spells turns gold into spell points. Collecting magic gems, roots, or other materials to cast spells turns those items into spell points. Even a spell failure roll, if it can put an end to your ability to cast one spell or all spells, is basically a spell point system with just one spell point.
But of course, calling everything a spell point system and looking no farther would be missing the point. It's not the points that matter, but how they interact with spells and with the game world in general. A pure spell point system involves a pool of abstract points that control when spells can and cannot be cast; it will also include a rule for how the pool may be refreshed. Either the control or refresh rules or both may be complicated by splitting the pool into two or more segments or by splitting spell casting or refresh into stages, possibly attaching different failure check rolls to different stages.
What non-spell-point systems do is connect one or more pools, casting stages, or refresh stages to something less abstract. For example, a Vancian system connects each individual "spell point" to a specific spell, selected ("memorized") before the adventure. A fatigue-based system connects the points to physical energy; running out of points is literally exhausting. A material component or scroll-based casting system turns each point into a physical object which can be stolen, sold, or given away.
To my way of thinking, making abstract components matter is always better.