What's the actual difference between Steuerklasse III/V and IV/IV?
Steuerklasse IV/IV withholds each spouse exactly as if they were single, using only their own income, so nothing is shared between spouses during the year. Steuerklasse III/V shifts the couple's entire tax-free allowance onto the higher earner (Class III), who is withheld using the marriage-splitting tariff on their own income, while the lower earner (Class V) loses their own allowance entirely and is taxed on a steeper curve with no tax-free band. The household's combined net pay is similar either way, but III/V front-loads much more of it into the higher earner's paycheck.