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Amps is the amount of current flow. Amp hours is how much total current a battery can provide. So, if your radio draws one amp of current a 7 amp hour battery could run it for 7 hours. If your radio draws 7 amps the battery would run it for an hour.
So, your three amp power supply can provide 3 amps forever because it is connected to the mains. Your battery has a limited amount of chemicals to produce electricity with and so is rated by amp hours, so you can figure out how long you should be able to run a device on it. Amps and amp hours, while related are two different things.
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