Well, here are the definitions I could find. Maroon is a bright, rich, deep, or dark red color, depending on which tone of maroon is in question; could also be purplish in color.
Burgundy is a deep shade of red. It is named after Burgundy wine. It can be a deep red, medium red or bright red in color.
So it looks like what separates the two of them is that possible purplish undertone in the Maroon. Otherwise, they are similar, but not likely interchangeable.