Why does a circuit breaker voltage rating differ between AC and DC?

An AC waveform consists of a (ideally, mostly) sinusoidal waveform that crosses zero voltage and current periodically.

All wiring has stray inductance, and when contacts are opened the inductance will cause a rise in voltage until there's an arc across the contacts.

There's plasma in the arc that makes the impedance between the contacts much lower than air, meaning the arc will tend to continue as the contacts move further apart.

With the AC waveform, the current crossing zero will extinguish the arc.

With DC, there's no zero crossing, so the contacts are limited to a much lower voltage so that the there's not enough electric field to keep the arc "lit" while the contacts pull apart.

Excess arcing is very damaging to the contacts, and will destroy the breaker if not controlled by observing the ratings.

There are special breakers and relays for higher voltage DC that use various techniques to interrupt the arc like magnetic coils to blow out the arc.

Interrupting DC is harder because there's no zero crossing to extinguish the arc. Therefore there's a lower electric field rating across the contacts for the same contact configuration.

When you open a switch, typically you get a spark. It may be a small spark you don't see, but it is still there. If there is enough current flowing at the time you open the switch, and if there are long wires or inductors connected, then that spark will turn into a full-on arc that bridges the gap and allows current to flow even though the switch is open or opening.

With AC, this arc will be interrupted when the current passes through zero. It will go out. And after that, the switch will be truly open. The arc cannot re-form. AC current stops and reverses twice per cycle.

DC is different. Once the arc forms, current flows through the arc and it can become self-sustaining. It will remain unless and until the contacts have moved far apart from each other, or some other technique is used to extinguish the arc. The arc can cause a lot of damage, melting metal, starting a fire, or violent destruction of a small part, causing little pieces to fly out everywhere. The higher the voltage, the worse it is and the farther apart the contacts need to be to extinguish the arc.

Switches and breakers and fuses generally have different ratings for DC for this reason.

Watch this video. Seeing is believing.

https://www.youtube.com/watch?v=Zez2r1RPpWY