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.