Switch ratings are related to the designed breaking capacity: it's much more difficult to break a circuit while current is flowing than it is to simply not impede flowing current while the circuit's closed, and prevent airgap breakdown when the switch is open.
Both current and voltage work together to create and maintain the arc of ionized air (plasma) that you are trying to break with a switch.
- As soon as you open the switch and the contacts stop touching, your load voltage will present itself across the switch and, when the contacts are still very close to each other, go beyond the airgap's breakdown voltage (goes up with the contacts distance, initially quite small). In any case, there is always some inductance in your circuit that will increase its voltage until the voltage across the switch goes beyond the air breakdown voltage . Reminder: this is because current cannot change instantaneously in an inductor: V=L*di/dt.
- At this time, the air between the contacts will ionize and turn into a plasma channel (fun fact: which has negative resistance, i.e. it conducts more and more with current) that will be bigger and hotter with higher load currents.
- That plasma will self-sustain until the contacts are sufficiently far away from eachother that the arc becomes unstable and eventually breaks: the breakdown voltage is already higher than the voltage the inductance can develop in the time it takes the arc to go away, thanks to the now-large distance between contacts. Natural air movement around the arc is usually enough, but you can blow on the arc yourself or with a fan to help (power plants shoot inert gases on the arc).
As you can see, in a nutshell:
- Higher currents tend to create a more damaging arc - possibly to a point the contacts melt instantaneously
- Higher voltages tend to maintain the arc for longer - possibly to a point the arc does not break at all
Some engineers only look at the load power vs switch breaking power but based on my understanding summarized above I'd say that's a dangerous assumption.
- AC inherently stops current midway through the wave frequency, so the arcs are rather easy to break
- DC never stops, so the switch has to do all the work. Arcs are stronger, for longer, which tends to weld the contacts or at least eat through them at each cycle.
So definitely don't make assumptions about DC based on AC rating.
Addendum: the ratings tell you guidelines to obtain an arbitrarily chosen design lifespan (this is what we call qualification) - don't expect them to last forever even if the ratings are met, or to fail only at that time, because the sparks erode and oxidize the contacts in an intricate way. You should be able to expect about half of those cycles with 99.9% probability assuming a gaussian (normal) distribution of failures, though.