What is the functional difference between a radical anion and a nucleophile?
Radical Anions are hundreds if not thousands of times more reactive
  than nucleophiles (right?).


Radical anions are very reactive, but some nucleophiles (such as $\ce{CH3^{-}}$) are also very reactive.

A radical anion is a molecule that has had an electron added to it.  For example, treating naphthalene with sodium in liquid ammonia transfers an electron from sodium to naphthalene forming the naphthalene radical anion, the electron is unpaired.

A radical arises from the homolytic breaking of a bond.  This process leaves an unpaired electron with each of the two molecular fragments.


  If an acidic organic compound is deprotonated to form a nucleophile by
  removing a proton, then is there not an unpaired electron availible?


Removal of a proton $\ce{H^+}$ (just a proton, no electrons) would leave 2 paired electrons (and a negative charge) on the remainder of the original molecule. 

Nucleophiles come in a lot of flavors.  They can be neutral, like the nitrogen in an amine, or they can be negatively charged.  If negatively charged, the nucleophile could be a radical anion or a carbanion.  So radical anions just belong to a sub-class of nucleophiles.  It's probably fair to say that carbanions and radical anions are usually better nucleophiles than a neutral nucleophile.  Comparing the nucleophilicity of a carbanion and a radical anion is harder to generalize since they are both so reactive, but the carbanion with 2 electrons would probably be more nucleophilic than the radical anion with one electron..