To bypass –– in one fell swoop –– the pratfalls of opportunistic demagoguery and mindless sanctimony, we direct people to the segmentations between numerous schools of egalitarianism:
Treats all moral patients as indistinguishable, apportioning the same quantity of a good per capita.
Treats all moral patients in accordance to their distinct needs.
It’s hard to overstate how useful it would be to have interlocutors who actually pay attention to “numerical vs. proportional” parameters instead of carrying on as if everyone holds same idea of what is meant whenever “equality” is cavalierly uttered. During political discussions, it would be doubly useful to qualify one’s views in this way.
Failure to conceptualize and frame the issue along these lines enables this type of irritable backwardness to turn up as the top result for "equity vs. equality" keyword searches:
There is no need for words like "equity" when we have Proportional Egalitarianism covering the same ground going all the way back to Aristotle. It would be a different story if all modes of equality had been conceived to march to the tune of Numerical Egalitarianism, which they weren't. So as things stand, equity = another case of word-abundance. There isn't a single mention of it in the SEP's lengthy article on equality and related concepts.
There's also the problem of equity being used varyingly depending on the region you're in. In the above image, equity corrects for natural disadvantages in ways that equality presumably cannot. But this tends to not capture ordinary people's view of equality, at least in my experience. People tend to think of equality in proportional terms more often than in numerical ones. Whereas when someone says "equity" or "inequity" around me, it's clear that they're referring to a meritocratic value / unmeritocratic disvalue, reserved mainly for the competitive domains of life.
The winner of an athletic contest, for instance, should be the athlete who outperforms all of the competitors, regardless of each competitor's sympathetic backstory, and regardless of who wanted the victory more. Any privileging of the losing athletes based on their having had worse struggles and sobs-stories would qualify as a strike against equity, rendering the contest inequitable on the whole. No one in my neck of the woods uses the word equity to refer to the elimination of natural bads, but it's how the above image would have us use it.
At the same time, athletic competitions start to seem insignificant when compared to competing political [distributive] theories. And at the same-same time, it's also crucial to acknowledge that our political aims don’t transition seamlessly into our ethical aims. There is a reason for why political philosophy is little more than a synonym for moral philosophy. A relationship between the two should no doubt exist, but this relationship must be a sinuous one. Legality has to do with civilizational strategy, which may ultimately (indirectly) lend a helping hand to ethical know-how. That's the goal, anyway. As such, every policy comes with teleological constraints, provided that politics ought to compliment ethics when all is said and done, which I believe should be the case.