First off, yes, it's fluorine and fluoride and not flourine and flouride. The mis-spelling is common, but the 'u' comes before the 'o'. Fluorine is a chemical element. Its anion, F-, or any of the compounds containing the anion are termed fluorides. When you hear about fluoride in drinking water, it comes from adding a fluorine compound (usually sodium fluoride, sodium fluorosilicate, or fluorosilicic acid) to drinking water, which dissociates to release the F- ion.