Anything expressed by DNA is a protein, but not all proteins are the same. Prion infections are caused by proteins that change the same proteins in the same way, like how crystals replicate.

A human analogy might be a disgruntled but charismatic worker who starts spreading a disruptive attitude until morale and productivity plummet in their department. As long as one of that team remains, the issue can still spread. Coincidentally, both the potted plants and highly compensated leadership are unaffected.