A linear power supply is extremely simple. It uses a transformer, diodes and capacitors and regulators to create a DC output from the incoming AC.
It's the oldest type of such converters and is in most high end audio gear.
A switch mode power supply is more complicated, much higher efficiency, much smaller, lighter and noise can really vary based on design. Done well it's noise can be equal to or better than the best linear supplies. Most are not done well. :)