What is the difference between a brie and a brie de meaux?

From cheese.com:

Brie de Meaux, named after the town of Meaux, is a French cheese produced in the region of Brie, located 50 kilometers to the east of Paris. [...] Brie de Meaux, an AOC cheese should be matured in the regions of Seine-et-Marne, Loiret, Aube, Marne, Haut-Marne, Meuse and Yonne.

See also Wikipedia.

So it's primarily a regional indication. Since it's an appellation d'origine contrôlée (AOC, "protected designation of origin") brie made in other regions can't use the name:

Under French law, it is illegal to manufacture and sell a product under one of the AOC-controlled geographical indications if it does not comply with the criteria of the AOC. AOC products can be identified by a seal, which is printed on the label in wines, and with cheeses, on the rind. To prevent any possible misrepresentation, no part of an AOC name may be used on a label of a product not qualifying for that AOC.

Brie de Meaux is an unpasteurized brie, with an average weight of 2.8 kg (6.2 lb) for a diameter of 36 to 37 cm (14 to 15 in). As for all other bries: they can be made from pasteurized milk, and they can be made anywhere (globally), so it's hard to make distinctions with them all. Usually, cheeses from unpasteurized milk have more flavour. As e.g. 'Life and cheese' writes in Beautiful Brie – raw versus pasteurised?:

Immediately you’re hit by the extra power of the raw milk. It has oomph. It intoxicates with its caramelised vegetal flavours, which relax into a savoury, umami tang, ...

Note that according to the New York Times (1981 post) Brie de Meaux in the United States is rarely the real thing:

But French restrictions on Brie labels do not apply in American markets, and cheeses labeled that way are probably not the same as they are in France. The United States Food and Drug Administration prohibits the import of cheeses made from unpasteurized milk that have aged less than 60 days. Since Brie de Meaux, the most popular type, is usually aged only about five weeks, the likelihood of any authentic Brie de Meaux being legally available in this country is virtually nil. Still, some of it manages to find its way to select shops and restaurants in this country.

Interesting read, confirming the US FDA rules anno 2016: Inside the World of Black Market Cheese

Brie is a large family of soft cheeses. “Brie de Meaux” is a specific type of cheese in that family. In France (and by extension the EU) but not necessarily in the rest of the world, “Brie de Meaux” is also a protected name and must come from a specific area and be made from unpasteurized milk.

The generic word “brie” also tends to refer to this particular style of brie but there are other “brie”, either protected (“brie de Melun”) or not. In my experience, cheeses called “brie” (with no other qualifier) are usually pasteurized and/or industrial versions of the “brie de meaux” but the word can also designate slightly different cheeses, sometimes produced with other ingredients (especially pasteurized milk but I also know some goat cheese brie for example). That's true both inside and outside France.

The taste and texture of an actual “brie de Meaux” from unpasteurized milk does differ significantly, not necessarily in a good way if you are not used to strong cheeses. Other types of brie you find in shops are almost invariably milder and less (able to) ripe.