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I would say that it depends upon the context in which these two terms are used. Many people, myself included, use these two words almost identically most of the time. We correctly might say, "The Godhead is a Trinity." Nevertheless, the two words are not necessarily identical. "Godhead" refers generally to all persons who comprise the one true God. "Trinity" has the inherent notion of "three distinct persons" who make up the one true God. There are some who deny the personality of the Holy Spirit, and others who deny the deity of Christ, so it is possible to believe in a Godhead made up of one person or two persons. It might also be possible to believe in a Godhead composed of more than three persons (though I can't think of one currently). Some people may even use the word "Godhead" to refer to a pantheon, a collection of multiple gods. But most people limit "Godhead" to one God comprised of more than one person, and the most common number of persons is three (Father, Son and Holy Spirit). Therefore, if one believes in a Godhead made up of one God existing in three distinct persons, they believe in the Trinity. To more fully or accurately define the biblical teaching on the Trinity, several other points must be added to our definition of the Trinity which further define the relationship between the persons of the Trinity (co-equal, co-essential, etc.). I hope these thoughts clear the water, Terry, rather than further muddying it.
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