To read charitably is to skip over, rather than use for your own rhetorical advantage, things in your interlocutor's words like ambiguity, awkwardness, slips of tongue, inessential mistakes. On the freeway of discussion, charitable reading is the great smoother-over of cracks and bumps of "I didn't mean it like that" and "that's not what it says". It is always a way towards a meeting of the minds, towards understanding better What That Person Really Wanted To Say - but nothing beyond that. If you're not sure whether something is a charitable reading, ask yourself if the interlocutor would agree - or would have agreed when you're arguing with a text whose author is absent or dead - that this is what they really meant to say. ... Now, going to the example in the post, where the ancient Roman chooses to interpret a progressive argument for increasing welfare as "really" carrying between lines the ancient Roman rationale. He is not doing a charitable reading of his interlocutor's words - they would definitely not agree that this is what they meant to say.

The first quote implies a subjective standard for charitable reading; charitable reading is when one reads the argument in a way they believe the other person would agree with. The second, on the other hand, implies an objective standard: a reading is charitable if it is what the other person actually would agree with. Can you clarify this issue?

Steelmanning, on the other hand, is all about changing the argument against your position to a stronger one against your position. The "against your position" part is left out of some good explanations in other comments here, but I think it's crucial.

If you end up being convinced by your own steelmanned argument, is that steelmanning? It's against your original position, but for your new position. Isn't there a temptation to come up with as strong as an argument as possible given the constraint that the steelmanned argument be just weak enough to not be convincing?