There are two options- an autotransformer and a triac phase control with a fixed setting to yield the correct RMS voltage for appliances such as hair dryers which are more-or-less resistive loads.
The autotransformer is a 60Hz type similar to this one from B&H Photo in NYC:
It may seem small for 50W but that's because it's an autotransformer (meaning it really only has to deliver 25W) and also it's pretty crappy- it will run warm.
The 1600W portion looks like the below (my own photo)
This is the internal circuit of an ordinary phase control dimmer used for incandescent bulbs with the knob and pot replaced by a fixed resistor (maybe) and trimpot. This is a particularly horrible construction and is not only unreliable but likely rather dangerous- The springiness in the leads is what keeps the triac in dubious contact with the silicone insulator and heatsink.
Here is the curve of RMS voltage vs. conduction angle from here:
As you can see, the conduction angle has to be ~65° and therefore peak voltage will be around 300V for a 230VAC mains vs. about 168V for a 120VAC mains.
If you run a 120V-only electronic device on the 1600W setting it could well be destroyed because it will see peak voltages well in excess of the rating.
There is very little need for either of these in 2021. You can buy compact travel dual voltage hair dryers and most electronics that would use the 50W setting is already universal voltage and only requires a plug adapter. I also would not want to try my luck with the hair dryer setting on a $500 CAD Dyson hair dryer.