You have all brought up a very important aspect about the specifications of components and how they relate to a component's application. As has been said, the ratings can be very misleading.
There is a surprising number of aspects to consider in the application of a relay and the closely associated simple switch, as has been mentioned already. In fact, contacts have caused more trouble than all the most complex integrated circuits put together, in my experience anyway. As well as restive loads there is the added complication of reactive loads, both capacitive and inductive, but on top of that there are low currents to consider. If the contacts are not of a suitable material, notably gold, too lower current will result in the relay contacts going open circuit because there is insufficient current to keep the contacts clean (the same with battery contacts on most remote controllers).
Some contacts have a high current contact with a gold flash over them. This type can be used for low currents, but once they have been used for high currents the gold is stripped off and they are no longer suitable for low currents.
The data sheets for power transistors can be especially misleading and the maximum power rating of a transistor is pretty much meaningless and in only a marketing ploy. The maximum current rating is similar.
kinarfi posted a very good example, the IRF2805 NMOSFET, but some of the new breed of MOSFETs are even more extreme. For example,
https://www.fairchildsemi.com/datasheets/FD/FDB016N04AL7.pdf
There are a number of factors that make these power and current limits fanciful: junction to case thermal resistance, case to heatsink thermal resistance, maximum junction temperature being one set. Secondary breakdown characteristics being the other main limitation. But then there are the basic problems of a high current which have already been mentioned: bonding wire capability, connections to the terminals, and the actual current capability of the PCB traces/wires. Even the solder melting as LG says.
In a juvenile moment we used to tack solder three wires to the pins of an inverted 2N3055 and see how long it would take to power itself off by melting the solder, or fusing and shorting out the power source.
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