This distinction is often confusing for architects, not to mention contractors and homeowners. A muntin is a small bar that separates two pieces of glass, aka "glazing bar" or "sash bar":
A mullion is a bar or post that separates two window units:
To add some confustion and a bit more complication, an astragel is the the same as a mullion except it sits between doors (it is the annoying fixed post you see between some pairs of doors that people often walk in to). Sometimes these are the projecting vertical bar or trim that is on the outer edge of one of a pair of double doors and is attached to the door.
And finally, a grille is a group of fake muntins. It actually does not separate anything but creates a pattern that simulates traditional muntins. These are usually plastic and below contempt.