It is eventually revealed that the real Adam and his mother were killed and eaten by ghouls seeking revenge against John Winchester. The "Adam" Sam and Dean were interacting with was a ghoul that had taken his form and memories.
While initially skeptical, Sam and Dean confirm Adam's identity through their father's journal and various "tests" (holy water and silver). Watch www xrysoi se Supernatural S04E19
Dean is infuriated to learn John gave Adam a "normal" life—taking him to baseball games and teaching him poker—while he and Sam were raised as hunters. It is eventually revealed that the real Adam
After a brutal confrontation where Dean kills the ghouls, the brothers give the real Adam a hunter's funeral pyre, officially acknowledging him as a Winchester. Key Episode Facts Watch www xrysoi se Supernatural S04E19