I think the assassin was different because she’d have died if she hadn’t killed him. Faith wasn’t under that threat from the deputy mayor

I’d say the closest example for Buffy is in Ted and the difference is that while Joyce tries to cover for her Buffy takes full responsibility and is torturing herself over it. The scoobies all agree that being a slayer doesn’t give her a license to kill and there’s no intention to just brush it off as nothing

In Consequences Buffy can see that Faith has put her walls up and is mostly just putting up a facade. When that drops slightly in Finch’s office Buffy tries to comfort her but then the walls come back up, she never wanted to punish her for it she wanted to help her - the problem was she didn’t know how to. Faith does some fairly terrible things after this in this episode but Buffy’s support never waivers because she knows that deep down what happened is hurting her. Faith even acknowledges in Choices when she’s fully gone over to The Mayor in her rant to Willow that they were trying to help her. Faith’s problem is not facing her own problems - not her fault I think it’s basically her coping method for how rough her life has been