[@Aphelion] First aid is a mundane skill, it's about how well the character can administer healing items such as healing draught, cure disease, antidote, etc and even helps to treat wounds without fancy concoctions. 

On the other hand, the Priest's Psalms are spells which heal, buff and protect. 

The Witch can't heal, her magic is dark and violent. To use game terms, the Priest has support spells while the Witch has aoe and burst attacks. 

EDIT: Oh, and if you're wondering if First Aid skill between different classes is any different, it isn't.