I would say that a “Jesus freak” is anyone who is a Christian and appears “too religious” to the person applying the term.
When I was in college in the late 60’s, the people we called Jesus freaks carried around leather-bound Bibles, but they never called them Bibles, but “the Word”, confusing the Bible with the “Logos” (“Word”) in the New Testament.
The typical Jesus freak in my experience emphasized spirituality over metaphysics.