Some sources seem to suggest that they are not, some suggest that they are but they are treated/processed differently.
I want to know if they are fundamentally the same grain, because they are very similar when prepared.
No. Bulgur is (almost always) made from wheat while barley is a different species.
Bulgur is cracked and parboiled before sale, while pearl barley has had the outer layers of the barley grain removed but is otherwise intact.