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I have a switch which reads 6A 125VAC / 3A 250VAC.
I can't figure out why this would be the case. The only reason I can think of the rating is the wires and contacts are only rated to take so much current and so much power dissipation. A higher voltage should not lead to more power dissipation. So why do switches and relays have lower current ratings at higher voltages?
I would imagine that the current derating at higher voltages would be due to arcing when the contacts open. Keeping the same current as voltages increase will allow arcs to persist longer and cause more damage to the contact surfaces. On small relays and contactors, these arcs are tiny, but if viewed in a darkened room, you can see that they do exist. Over several thousand cycles, (especially with inductive loads such as motors) the arcing will cause pitting and oxidation of the contact surfaces. Damaged surfaces are more resistive, which heats the contacts, and promotes more arcs. Failure will come much sooner under these conditions of accelerated wear.
The information you see on a relay is really a condensed from of what is called a load limit curve. It's better to really think that the relay can switch a maximum power, rather than a given current and voltage. To a large extent, this limit is due to arcing - both from the point of an arc forming and being sustained and destroying the relay, or in terms of the contacts becoming pitted and not reaching the rated number of switching cycles.
If you take a look at a data sheet e.g. this one on page 7, you will see load limit curves. In the top chart, they have drawn a constant power line at 40W, which is entirely below the load limit curve. This means that the switching capacity of the relay is 40W across the range.
The switching capacity is the largest DC load that the relay can switch, irrespective of current or voltage. It has nothing to do with power dissipation in the relay itself, which should be minimal. The quoted numbers on a relay are generally just indications of current at line voltage in a few countries.
Load limit curves can be derived experimentally, but I think quite a few are just based off theory on switch geometry, contact material, speed of opening etc.
At the extremes of very low current and low voltage, arcing isn't as much of an issue, so the rating will be slightly higher here.
DC is more prone to sustaining an arc than AC, so the curve is for DC. Sometimes they also show lines with derating applied for inductive loads.
6A @ 125V (assume DC for simplicity) is 750 Watts. 3A @ 250V = 750 Watts That sis why they have same rating. Its expressed this way because this switch is designed for switching mains current. In USA thats 115V and in UK/Asia its 230-250V So the manufacturer is trying to help you select this switch based on your current draw. The same applies to wiring in the USA and elsewhere. In the USA you need a thicker cable to carry more current at a lower voltage than in Europe (for example) - all to supply the same power.
But we generally do not rate these items by power - so the conversion to V/A is printed to make your life easier.
