Fitch for Propositional Logic (FitchPL) is the Fitch proof system with the propositional rules.
Fitch for Herbrand Logic (FitchHL) is the Fitch proof system with the propositional rules, the quantifier rules, and the induction rule.
Fitch for First Order Logic (FitchFOL) is the Fitch proof system with the propositional rules, the quantifier rules, and the equality rules.