Is there a difference between Density and Specific Gravity?
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.