OK, so in conclusion if we have a power supply rated at let's say 5 volts and 5 amps it means it is rated to deliver a maximum voltage of 5 volts and a maximum current or 5 amps. When connecting devices to that power supply if they require 5 volts at less than 5 amps they will run just fine. The device will only draw its rated current from the source (power supply). Much like the battery in an automobile. The battery is capable of supplying hundreds of amps but the automotive systems only draw what they need.
However, if we take that same 5 volt 5 amp supply and try to power a load rated at 5 volts and 7 amps this will create an "over current" condition. The load requires more current than the source can supply. This is where bad things can happen. A good quality power supply will shut down and use protection when an over current condition exist. The voltage out will fold over and drop. Lower quality power supplies sans protection will in many cases just burn up if they are not fused.
Ron