When we visited France, our friends told us it is primarily a regional difference, and how they eat it is very different, as well.
Both are not eaten until they become "ripe." That means when you press on the outer skin, it "gives" under gentle pressure. If you purchase it unripe, you can make it ripen faster by keeping it out of the refrigerator.
Once it's ripe, eat right away.
Brie is eaten at room temp with loaves of crusty French bread. Cut into triangles, eaten with the chewy, outer skin. (don't dig out the soft center: bad manners) Brie has a creamy taste.
Camembert is soaked in water inside its round, wood box; then buried in the coals of a fire. (If it comes with a wrapper, remove the wrapper first!) After about 5 or 10 minutes, pull the box, with the cheese in it, out of the fire; let cool; open and enjoy with French bread. Camembert has a nuttier taste, but is also wonderful.