Tourmaline is actually a group of minerals in the cyclosilicate family.  This is a rather new mineralogical designation, referring to the fact that the silica tetrahedra (SiO4) - the basic building block of all silicate minerals - form distinctive open rings that translate into structural tubes in three dimensions.  In Tourmaline, these rings are the owed to the presence of the element Boron, which pulls in three oxygen atoms, each of which is a member of a separate silica tetrahedron. It is the repetition of this structure that forms the rings.  Beryl is another cyclosilicate, and similarly, it's structure is based on the presence of Beryllium, which also forms these three-fold coordinated tetrahedra.

Contrary to Beryl, Tourmaline can contain a wide variety of other cations (positively charged metal ions), and mineralogists make the division of Tourmaline based upon what those cations predominantly are.  The chemical formula for the group is often listed as:

XY3Z6(BO3)3(SiO3)6(O,OH,F)4

Meaning there are, in addition to the Boron and Silicon, three possible structural positions (X,Y, and Z) for other cations.  Based upon their size and charge, different elements can fit into the structure and balance the electrical charge.

The following are the three most common Tourmaline minerals and their X,Y3,Z6 position cations:

Elbaite:    Na,(LiAl)3,Al6
Schorl:    Na,Fe3,Al6
Dravite:   Na,Mg3,Al6

Less common are:

Liddicoatite Ca,(LiAl)3,Al6
Uvite:     (Ca,Na),(Mg,Fe)3,(Al5Mg)6

Note that these are considered "End Member formulas, meaning that there is often a continuous solid solution between these "perfect" formulas. You could easily have a nice, gemmy Tourmaline, whose chemical formula puts it smack dab in the middle between Elbaite and Liddicoatite.

Rarer still are Chromdravite, Feruvite, Olenite, and others.  These are all mineralogical designations, based upon chemical content. 

The gemological references often include color-based names, usually for the gem varieties such as:

Rubellite:  Pink or red tourmaline (usually Elbaite but possibly Liddicoatite)
Verdelite:  Green Tourmaline
Indicolite or Indigolite:  Blue Tourmaline
Achroite:  Colorless Tourmaline

Tourmalines can be almost any color, but not every color has a name.  It's fair to call a yellow Tourmaline "Yellow Tourmaline".  The point gets across without too much fuss, but if that's not sophisticated enough, you can call it "Tsilaizite", (a reference to the place where much of it originates).  Sometimes locality-specific names get into Tourmalines when they have a definitive color or chemistry or both, as in the case of "Paraiba Blue Tourmaline" - so named because the high copper content (though in extremely minor amounts), generates a very intense blue color.  Yet not all "Paraiba Blues" come from Paraiba.

And let us not forget Tourmalines of multiple colors.  Elbaites and Liddicoatites commonly range in color from green on one end to red on the other, or many combinations of this.  A Schorl may have a blue or purple tip.  These are all grouped as "Bicolor" or "Multicolor", and they are not as rare as one might be led to believe.  A subdivision of these are the "Watermelon" or "Reverse Watermelon", which range from green to red from the interior of the crystal to the outside.

But they are all Tourmalines.  The point is:  Don't be fooled into believing that some name or designation automatically results in a higher price.  Your best guide is the look and size of the stone itself, regardless of its name.