Salinity is the salt content within the water. This is usually measured with a refractometer (accurate up to like 99.9% or something like that when device is calibrated right). Light travels through water differently with the amount of salt content. So really the measurement is how light travels through the water, and light really can't be wrong.
Specific gravity is how boyant (sp*) things are in water with a certain amount of salt content. This is usually measured with a hydrometer (not very accurate). Different densities of salt (because of content) make things float/slink differently. The trick with specific gravity is you have to take into account heat/temperature of the water. PHysics 101 tells us that water molecules will contract when heated and expand when chilled. So much higher temperature things will be a bit more boyant. So when measuring specific gravity you have to take into account temperature and salt content.
Hope this helps.
Disclaimer: I realize dark, sep, and a few others will jump in here and correct me, i'm sure i got a few things wrong but you get the general idea.
BUY A REFRACTOMETER - THIS IS THE ONE CONSTANT THAT MOST WILL AGREE WITH.