Power adopters convert 220/110 volt domestic AC supply to small DC voltage suitable for your equipment.
Since the device work on different voltages and have different power capacity, the plug which goes to your equipment is different for each. This is to prevent from wrongly connecting to higher or lower voltages.
Most power adopter outputs are 6volt DC 12 Volt DC etc.
picture credit circuit diagram.org.
Transformer converts 230 volt ac to 6 volt AC..Diodes convert 6Volt AC to 6 volt DC.