Extending gas duration is the main draw to rebreathers, that is correct.
In case of O2 rebreathers and closed circuit rebrathers it's actually oxygen that is added, as much as needed to replace the O2 that is metabolized. Hence the enormous gas savings, especially at depth. Mixed gas CCRs use a diluent to make up for pressure volume changes and to keep the gas breathable at depth. Since it's rebreathed savings here are also considerable, very much so if you use helium mixes. Depending on the amount and type of diving done a $10K rebreather/training can pay itself in gas savings in a year or two.
Semi-closed rebreathers usually use a pre-mixed gas, same as open circuit diving, but extend somewhere between 4 to 12 times, depending on the system and setup. All of them use CO2 absorbant, either in granular or cartridge form to remove the CO2.