The little metallic knob is the screw; it is used to tighten and loosen the hairs, but, even though the two are sold as a unit, I don't know if the screw is technically considered part of the frog. Of course, if the little bull's eye decoration is the frog as in military dress, that could throw me back to the saber anchor.

The flower things are probably called frogs because they're green and they sit in the water. Something you'd say to a kid, kind of.