The ARM is essentially a semi auto version of the basic Galil infantry rifle, with a folding bipod, a wood forend that the bipod folds up into, and a carry handle at the rear of the forend (every Israeli soldier I ever knew or saw takes the carry handle off 5 minutes after being issued a new Galil).
The AR was a US legal semi auto version of the Galil carbine, which was issued to officers and crew served weapons people. The issued version has a 13 inch barral, to short for legal importation, so IMI simply put the rifle length barrel on the AR, making it legal for civilian import here. Differences from the ARM are a plastic forend, no bipod mounting lug, and no carry handle. The original importer,Magnum Research, also offered a model which they called the AR/M. That was an AR, with the bipod mounting lug on it, so you could purchase a kit containing the bipod, wood forend, and carry handle and swap back and forth.
The .308 versions were also offered in the three variations noted above. In terms of the Israel Defence Forces use of the .308, they were used only as sniper weapons and issued with one version or another of special stock and sight arrangements, so the US imports were basically a "downgrade", since the standard stocks they were sold with over here weren't actually used on the .308s used by IDF. Actually the sniper .308 Galils weren't used very long by the Israelis, once they discovered the US M14.