There's a much more important (though somewhat cynical) distinction between the two though. A contractor is a guy working for your company on the equivalent of a 1099, who behaves much like an employee. A consultant is an outside entity who comes in to do a specific piece of work, and tends to be treated as something of a specialist who you should listen to. Given that the actual work being done is usually indistinguishable, guess which one you should call yourself if you want to make more money?

There's a 3rd term for this same position, "Freelancer", that you can use if you want to make significantly less than either of the above.