There are different ways of reducing low voltage (230v) to extra low voltage (12v) the simple method is a transformer and I had an old Ikea reading lamp which did have a simple transformer these should would with LED as well as tungsten lamps I have swapped my 4 x 60W for 4 x 0.58W and they worked for quite a time before the lamps failed one is still working and likely they failed because poor quality rather than anything wrong. But one has to be careful as transformers give an AC output where LED's use DC so the peak voltage of 12 volt RMS is around 16 volt and some poor quality lamps can't take the peak voltage.
LED lamps are different from LED's in the lamp has a built in driver so although the LED is DC the lamp could be AC or DC or both, I have bought some LED lamps clearly marked AC.
The whole idea of reducing the voltage to 12 volt was to extend the life of the quartz bulb it may have also been desirable in bathrooms to have SELV (separated extra low voltage) but main idea was to extend the life of the quartz bulb. It was better if the output from the voltage reducer was regulated so there was a move to using switch mode or pulse width modulated (really the same thing) power supplies which were often labelled as "Electronic Transformers" these units often have a minimum as well as maximum load they give out AC but this may be at a higher frequency than our mains supply and also likely not sinusoidal but this does not matter for a quartz bulb. However with an LED bulb the peak voltage could be well over 16 volt so they also could damage the bulb.
The LED itself requires a driver built into the bulb a drive controls current not voltage but because the unit which controls the LED directly is called a driver it seem manufacturers are also calling any device used to drop drop current or voltage associated with LED's as drivers so one has to be careful to buy a power supply with a voltage regulated output when using it with bulbs which already have drivers in the bulb and vice versa with LED's without built in drivers to get a current controlling power supply for that type.
So forget the names look for 12 volt and AC or DC according to bulb type. Normally a 12 volt DC power supply is used with 12 volt LED bulbs as this ensures the peak voltage is within limits. In the main better with the exception of special locations like bathrooms to move to low voltage (230 vac) rather than use extra low voltage as there is then no problem ensuring everything matches.
I selected an Ikea Bulb
to see what it said about the bulb. Under the technical information it:-
Does not state voltage.
It calls it a MR16 when it clearly does not have any reflector.
Gives 3.5W and 200 lumen.
The latter means 57 lumen per watt which is about the worst lumen per watt I have found. My lamps vary from 60 to 100 lumen per watt at low wattage the lumen per watt goes down so 1.8W 60 lumen per watt normal but at 3W looking at 70+ lumen per watt and at 24W looking at 100 lumen per watt. So it would seem Ikea LED lamps are very poor quality. There are also losses in the voltage dropper so in real terms it will be worse than 57 lumen per watt.