As to muntins vs mullions, since we are being pedantic, I looked it up in the third edition (1944 with corrections through 1964) of the Oxford Universal Dictionary. I figured that would be old enough to have the definitions as they 'used to be.'
Mullion: A vertical bar dividing the lights in a window, esp. in Gothic architecture; also, a similar bar in screen work.
Muntin: A central vertical piece between two panels, the outside pieces being called stiles.
That definition of muntin is the one I know from my old books on cabinetmaking and millwork- it is the center vertical piece in a paneled door (and yes, the outer framing pieces are styles, the top and bottom horizontal pieces are rails.
Now, as to what the horizontal piece between window panes is called, I forget.