Yes, ιουδαίος is the person that believes in Judaism or is a Jew (but is used mostly with the first meaning). Εβραίος is a person that is a Jew.
Εβραίος generally refers to all Israelites, including the lost tribes. Today it is used to refer to the Jews, but the old meaning still applies. Ιουδαίος is more correct, and just like troll1995 said, this applies more to the religion than the national term.