There are two types of solar powered lighting shown in this diagram. At the top there is a collection of AC bulbs powered by an inverter and below two DC 12v bulbs connected to the output of the solar charge controller. This output is often electronically switched in such a way as to protect the battery from deep discharge (which could damage it) Good quality inverters also have deep discharge protection.
Inverters used to be much less efficient than they are now so the losses outweighed the advantages of being able to use low cost lamps, switches and cabling. Modern inverters also have a standby sensor circuit which only starts the inverter when there is a demand for some power.
Solar lighting kits can be either AC or DC or indeed both but it's much easier to integrate a solar lighting kit into your existing mains wiring if you use a good quality inverter.
The charge controller in the above diagram has an output specially designed for low current devices like solar lighting and has an integrated button to switch the lighting circuit on or off. If you accidentally leave the solar lighting on the controller protects the batteries from deep discharge by witching the light off id the battery voltage becomes low. It's a Steca PR 2020