I guess this is why they call it a switch mode power supply.
Yes sir.
And as soldar stated above, several kind of SPS (Switching Power Supply) exist (it is sometimes called 'topologies') and those can use different 'modes'.
Many SMPS (M =
Mains Mode) for computers use the 'flyback' topology (1).
Today, an additionnal stage is often added between the input rectifier and the switch : it is called the '
PFC' (Power Factor Corrector). It becomes compulsory because it limits the pulse currents drawn from the mains.
There are also more basic SPS topologies that do no use transformers, but only inductors (usually a part with only two connexion wires). If you want to dig into that subject, you may google for the words 'buck' or 'boost'.
(1) You may find interesting to follow this
thread where several members try to provide some help in order to repair a badly damaged flyback. But it's not an easy task.