That is called a SAW.
Full auto, yes. Belt fed? No. The M1918 BAR is fed with a 20 round box magazine, and at one time had a 40 round box magazine.
The BAR has never been belt fed. I think you're confusing it with the Browning Model 1917 .30 cal machine gun, which was belt fed.
There was never a belt-fed BAR.