What is the difference between a switch mode power supply and a transformer power supply?

Comparison: transformer power supply vs. switched-mode power supply

Unlike conventional power supplies with 50- or 60-Hz transformers, less magnetic volume is required for the same power due to the conversion to higher frequencies.
In the switching power supply, the transistor is always completely blocked or completely open and is therefore hardly heated. Thus, high efficiencies above 90% can be achieved. The disadvantage is that the circuit must be well shielded because of the internally used powerful AC frequency to ensure good electromagnetic compatibility, and that at the output is always a small proportion of this AC voltage measurable. This disturbs less digital circuits or chargers, but very much sensitive amplifiers e.g. in radios, hi-fi systems or EEGs.