I am trying to learn the anatomy of the brain and am getting rather confused. When it comes to the brain stem, I have seen some sources say that it consists of the midbrain (mesencephalon) and hindbrain (rhombencephalon). However from what I understand, the hindbrain consists of the metencephlon, which is comprised of the pons and cerebellum, and the myencephalon (medulla oblongata). So these sources seem to say that the brain stem contains the cerebellum. However I have also seen sources say that the brain stem consisists of the medulla oblongata (myencephalon), midrbrain (mesencephalon) and pons, so it excludes the cerebellum.
The brain stem comprises the medulla, the pons and the midbrain, according to Kandel's extremely authoritative Principles of Neural Science. This is equivalent to the midbrain and the hindbrain minus the cerebellum, which is probably where the confusion stems from.
Kandel, E. R., Schwartz, J. H., & Jessell, T. M. (Eds.). (2000). Principles of neural science (Vol. 4, pp. 1227-1246). New York: McGraw-Hill.