Is there a difference between Density and Specific Gravity? My textbook says that the specific gravity is "the ratio of the mass of a mineral compared with the mass of an equal volume of water."

Is this any different to density? If so, how? If not, why does it have its own name in geology?
It is different to density but they are closely related. This is easily seen by considering the dimensions of the two quantities (side note: always consider the dimensions of quantities - it is invariably useful).

If you read your definition carefully you will realise that specific gravity is defined as the ratio of the density of the material to that of water. $$\mathrm{SG = \frac{\rho_{sample}}{\rho_{water}}}$$

Historically I suspect that specific gravity was used rather than density because it is easy to measure by measuring the mass of the displaced water when you place the sample into a jar of water, and the mass of the sample itself. You don't actually need to know the density of water in order to calculate the specific gravity.