A score is a numerical measure of some aspect of a character. Scores are determined when they become relevant to the character and changes to a score are changes to the character. For instance, you determine a character’s Strength score when you create the character, and changes — ‘permanent increase’ or ‘permanent decrease’ — are uncommon. Scores may be prerequisites for gaining abilities: in first edition, you must have a Strength score of 13 or more to gain the Power Attack feat.
At this point I see no reason to change from the classic Strength, Dexterity, Constitution, Intelligence, Wisdom, Charisma set, on a nominal 3..18 range, with modifiers equal to floor(score/2-5). There is a lot of inertia here.
Because I am that old, I like the even more classic modifiers (3: -3, 4..5: -2, 6..8: -1, 9..12: +0, 13..15: +1, 16..17: +2, 18: +3) but I don’t think I’ll do that now.
I might decide to go the AGE System route and reduce scores to just what are now modifiers, but for now I’m sticking with nominal 3..18 range.
Ability score generation to be determined. As someone who designs systems for a living I like the control inherent in point buy, but as a GM who regularly needs kicking out of a rut I like some randomness to it. My preferred ability score generation rules have elements of both.
For now, sticking with Fortitude, Reflex, and Will. They can apply to more or less any genre I can to consider.
A pool is a resource, usually a count of something, that can fluctuate quite a bit during play. A character does not have a pool until it becomes relevant to the character, as from gaining an ability that uses that pool. The current value of a pool will not be a prerequisite for another ability, but the presence or size of a pool might be. For instance, you must have a ki pool to gain ki powers. You may need to spend pool points to use an ability, or you might need to have a certain number of points available (but not spend them) to use an ability.
The size of a pool is a score (numerical measure of how big the pool is and does not fluctuate much in play), the number of points in a pool is not. In fact, measurement or counting of ‘points’ might be one of the key indicators that we’re looking at a pool rather than a score.
Hit points are a pool measuring a creature’s ‘hard to kill‘. They don’t measure meat or the capacity for physical trauma, many ‘hit point losses’ are situational rather than actual trauma. The values fluctuate throughout an adventure, and even throughout an encounter.