One aspect of the Strength score. One of its effects
They're not even close to being synonyms:
Aspect: a characteristic to be considered
effect: a phenomenon that follows and is caused by some previous
phenomenon;
My reasoning is that you only get the +2 effect when you have the appropriate Strength score, not the other way around. The +2 modifier is one of the effects of being that strong.
Your reasoning is wrong: if I tell you that a character has a +2 ability bonus, it means that he has a 14 or 15 in that ability. There's a correlation between the two representations, but this does not constitute a causal relationship. The +2 ability bonus and the 14-15 ability score are just two representations of the character's inherent strength.
There is no "getting" of the bonus, in other words. There's only how we describe the same amount of strength in different contexts.
Without the appropriate Strength, you do not gain the bonus; you would not say it the other way around, nor is it logical to think of it that way.
Incorrect. Having that strength score is the same thing as having the bonus. You don't 'gain' or 'get' the bonus. You already have it when you have that score.
The moment when the strength score provides the bonus
doesn't exist. Because that bonus is already there--always. The one is just a translation of the other: the bonus is just a way of saying how you apply the character's strength score to various rolls.
If I grew a pair of wings, I could fly. However, I do not grow the effect of flight--that is the effect granted by the wings.
No! This is the real crux! You grow wings as a result of something else other than the act of growing wings. 'Growing wings' is a phenomenon that results from another phenomenon. Whether you use them to fly or not is irrelevant--it doesn't matter if there's an 'effect of flight'.
But this is a game, with mathematical mechanics. The feats are the source of their effects.
Do feats come from nowhere? Are they unmotivated motivators? No; the character receives them from some other action. They are the results of, the
effects of some other action.
If a character levels up and says, 'I want my guy to have the ability to brew potions,' and the DM says, 'ok', then the guy now has the ability to brew potions.
That's all that happens. There's no intermediary, no extra step.
Not even when you codify that process as taking the Brew Potion feat.
Look; the problem, I think, is that people look at feats as if they were spells. They're completely different. If a feat has a parallel with any part of the spell system, it's with the numbers in spell slots.
So:
Ragnar is a character who 'can cast 4 third-level spells'.
Ragnar is a character who 'can brew potions'.
Ragnar is a character who 'adds 4 to his initiative rolls'.