What is the meaning of output voltage and current?
The 5V power supply is regulated, meaning that its internal circuits will hold the output voltage at about 5V for any output load current up to 1500mA. It's really not a matter of having less internal resistance, it has feedback circuits that maintain the desired output voltage.

The 9V battery is unregulated. Sure, you may have measured 3A when you shorted the battery with your meter, but the output voltage from the battery was very small. The internal resistance of the battery is a factor, but physical size is also important. A battery provides power from a chemical reaction, and the more chemicals you have available to react the more current you will get.