A REx electric car is a Range Extender type of PHEV. It has similarities to a normal PHEV in that you plug-in to charge, and also has a petrol motor which is fuelled in the normal way.
However the way they work is different. The petrol motor in the REx car is much lighter weight and smaller, and doesn’t drive the wheels directly. The car runs on battery in EV-mode until the battery has nearly run out; the motor then automatically kicks-in to recharge the battery.
Obviously this has the advantage in being able to refuel from any petrol/gas station as an emergency measure. The disadvantages are it adds weight which reduces performance & the EV-only range. They are fairly complex so the maintenance costs can be high.
The BMW i3 was originally released in ‘pure’ EV and REx versions, the REx used a small motorbike engine developed in Korea. The REx version is no longer available to buy new, because battery range has improved to be the same as the REx.
The other common range-extender vehicle is GM’s Chevrolet Volt (Opel/Vauxhall Ampera) which is no longer on sale.
On balance this is a good option if you want to drive mostly on battery with very occasional need for longer range and don’t mind the extra servicing costs. As an example a neighbour has a REx car, used mostly for work, and he has put petrol in it an average of 3 times a year. An alternative option is you could have a battery-only EV and rent a car for those long trips.