Three things on the buttons front are clues to its civilian origins, First is the lack of detail in the eagle. Second is the shape of the anchor and the anchor fluke in front of the wing although there are specimens of Navy buttons with the fluke in front of the wing. And Third the anchor eye does not extend to the edge where the rope border runs through it.
Going by how nice your button is I would say the back is there. Please post a picture of it.