I'd break social skills down into Guile, Presence, and Empathy.
Guile covers manipulating people to give you what you want. It's an active, offensive skill. That makes it sound a little negative, but that's because it's self-serving. If you're out there being generous there's likely not a reason to ROLL anything. Manipulation, persuasion, lying, bluffing.
Possibly disguise as well. You are
convincing the target to change
their mind.
Presence is first impressions, intimidation, provocation, public speaking. Loud, overt displays of social prowess. You are
forcing your will upon your target, and making their mind up for them because the alternatives are not as interesting / too scary / too shaming to accept.
Empathy I see as more defensive/detection-oriented, and doesn't need too much changed IMO. It's just kind of wishy-washy when you would use it to "attack" is all.
I don't think I would mess with the Skills very much, though certain other tweaks I use kinda change how the Skills are used. For example I kinda changed Mental and Social stress a bit in that Social stress is only inflicted by attacks meant to change the character's image, whereas Mental stress is inflicted by attacks meant to change the character's mind.
This makes Conviction useful in making an unflappable character, as it should be, and it also makes persuasive characters more powerful against casters, since they can throw them off their game with Mental attacks.
FWIW, and regarding Conviction, I try to get an idea of what each of my PCs' Conviction is actually about. What DO they believe in? And then I let them use Conviction to defend against any social stressors that would directly affect that belief if they want. Otherwise, yeah, I generally agree with Opidiomancer. I know my POV of where the Mental/Social Stress tracks divide isn't exactly RAW, but I like that "Composure / Reputation" feel more than the "Psyche / Everything that's not the former" feel.
Finally, I freely admit you can come up with examples that my model doesn't work with either. That's true for anything anyone's going to come up with.