IV/IV is the neutral default: the Finanzamt withholds each spouse exactly as it would a single person, using only their own income, and nothing is shared during the year. It's a fair, predictable starting point, but it can leave a household under-withheld or over-withheld relative to the couple's real combined liability whenever the two salaries differ meaningfully.
III/V is a deliberate reallocation. The couple's entire tax-free allowance moves onto the higher earner's paycheck (Class III), who is taxed using the Splittingverfahren, the same marriage-splitting math the final annual return uses, applied to their salary alone. The lower earner (Class V) loses their own allowance in exchange and is withheld on a steeper curve with no tax-free band at all. The net effect is more cash landing in the higher earner's account each month, less in the lower earner's, with the household total ending up similar either way.
What never changes is the real bill. Ehegattensplitting, the joint-assessment mechanic settled at tax return time, calculates the couple's actual liability from their combined income regardless of which Steuerklasse combination they picked for monthly withholding. III/V and IV/IV are purely a cash-flow choice: how much of that eventual liability gets withheld now versus trued up later, and, with III/V, by law.
That's also why III/V comes with a mandatory Steuererklärung: its withholding is a rough approximation that rarely lands exactly on the final number, so filing is required to true it up. Couples who want to avoid guessing can also ask their Finanzamt about IV/IV with Faktor, a third option (not modeled here) that applies a personalised multiplier to track the real liability even more closely than plain IV/IV, without III/V's aggressive skew.