What is the difference between excuse and recuse?

Recuse is a legal term used when a person disqualifies oneself (as a judge) in a legal case due to a potential prejudice or partiality. Example: The judge recused himself from that case, citing a possible conflict of interest.

Excuse is to release a person from an obligation or duty. Example: The gentleman is excused from jury duty as his serving would cause a hardship for his family.