There are two varieties of the Brussels Griffon here in the U.S.  The Brussels Griffon
and Petit Brabancon.  The (rough) Brussels Griffon has a  long, wiry coat with
fringe around the face.  The (smooth) Petit Brabancon has a short, smooth coat. 

The Brussels Griffon was first shown at the Brussels Exhibition of 1880.  An early
example of the breed is depicted in a Van Eyck, the Flemish painter.  Once kept by
coach drivers of 17th-century Brussels to rid their stables of vermin, the
Brussels Griffon became a companion breed by virtue of its appealing character.

The Smooth coated Petit Brabancon probably owes its existence to the introduction
of the Pug.  The Pug introduced heavier bone, broader skulls, and an overall sturdier appearance to the breed. 

AKC recognizes only the breed known as the Brussels Griffon.
Its American standard allows all of the color varieties, black through red,
as well as the smooth variety (Brabancon).  Roughs are often
bred to Smoothes to produce deeper coat colors.

FCI (Europe), conversely, divided them into three breeds: smooth (Petit Brabancon),
rough reds (Brussels Griffon) and roughs of other colors (Belgian Griffon).
Therefore, in Europe they are shown separately with no interbreeding
between the varieties.