* Hoenheim is the father of Edward and Alphonse Elric. This is established early in the series and is undeniable.
* "Father" is a separate entity, an artificial being who calls himself "Father." He is the ultimate antagonist in Fullmetal Alchemist: Brotherhood.
* "Father" was created by the original "Father" - the entity who created the world. This original Father was the one who bound Hoenheim to the Gate of Truth and essentially split him into two separate entities: Hoenheim, who remained in the human world, and the entity who would eventually become "Father."
* "Father" is ultimately not the biological father of Edward and Alphonse. He was created as a separate entity from Hoenheim.
So, while Hoenheim is the biological father of the Elric brothers, "Father" is not their biological father. However, he is directly connected to Hoenheim and therefore to the Elric brothers, making him a very relevant and complex figure in their lives.