There are different Herods in the Bible. We have Herod the Great who ruled when Jesus was born and Herod Antipas, who ruled later.

I have seen in several places that Herod the Great is called "king" and Herod Antipas is called "tetrarch", apart from some texts written with simple language like Gospel of Mark where he is also called king.

My question is – was Herod Antipas a true, "full" king? Or does his title suggest that he was someone lower than king? Was he coronated? Is a tetrarch a king or something more like a prince or duke?