Is there a difference between polarity and hydrophobicity?
Hydrophobicity means aversion to water which results because of increase in entropy of the system due to the water-"solute" interaction. 

As already pointed out in by inf3rno, polarity of a molecule is because of its net dipole moment. It is true that polar molecules can dissolve in water (because they can interact with water via van der Waals' forces especially Keesom and Debye forces).

CO2 is apolar but dissolves in water (it actually reacts with water). Most apolar substances cannot interact with water via van der Waals forces.

To sum up, usually polar substances are not-hydrophobic (i.e they are hydrophilic), however some polar molecules such as nitriles, ketones and esters can be hydro-neutral (midway between hydrophobic and hydrophilic. See here). Even large polar molecules are insoluble in water such as 1,2 dichlorobenzene and nitrobenzenes (For something to be soluble the solute-solvent interactions should be stronger than solute-solute interactions. "Water insoluble" may not be equivalent to "hydrophobic").

Conversely, apolar substances are hydrophobic (unless they are reactive solutes such as Cl2 and CO2).