For an AC to DC power supply, there are several approaches that can be taken to provide the desired output. These approaches are not at all equal and have rather significant benefits and drawbacks. The two most popular types of power supplies are linear and switching power supplies and they work completely differently.
A linear power supply would perhaps be considered the typical method of creating a lower, DC voltage from an incoming AC voltage. The signal is routed through a transformer to drop the voltage, and then put through either a half or full wave rectifier, before being filtered and output. Due to the usage of a transformer, these power supplies are generally larger and heavier and this method is also not very efficient. However, they are quiet electromagnetically and are ideal for applications that require clean, low-EMI power.