According to the definitions in Oxford Dictionaries: "confessor" is a priest who hears confessions and gives absolution and spiritual counsel but can also be a person who makes a confession. "confessant" is a person who confesses to a priest; a penitent.

What is it called when someone confesses?

"namesake"): Both the person confessing and the person hearing the confession can be called a confessor. Per Oxford Dictionaries, the term is probably applied more often to the person hearing the confession: A priest who hears confessions and gives absolution and spiritual counsel.

Is confessor a word?

noun One who makes a confession.