[firefly5]

*ding ding* Artist chiming in!

"Maroon" is derived from French marron ("chestnut"), it became a color-word in English ca. 1791.
"Burgundy" is a region in France ironically best known for their white wines (i.e. Pouilly-Fuissé) however the color-word refers to the red wine. The first recorded use of burgundy as a color name in English was in 1915.

So I would say they are both deep reds, maroon has a more brownish tone, and burgundy more pink/purple.
However if you want to match/co-ordinate I would not recommend buying without comparing colours directly in real life, as they are very difficult colours to match up.