The term halide-free was developed many years ago by the IPC when no-clean fluxes were created. It is well known that halide ions can cause catalytic corrosion which will cause an electrical failure in an electronic device. Therefore, you do not want halide ions floating around in the flux residue on the board. Halide ions are a result of using a compound containing Cl, Br, F, or I with an ionic bond. Ionic bonds are easily broken creating the halide ion (i.e. Cl-). The IPC J-STD-004 has a test that ensures that the flux does not contain an ionically bonded compound containing Cl, Br, F, or I.
Halogen-free was developed as a result of environmental concerns with Cl and Br. Today, most definitions of halogen-free for electronics are only incorporating Cl and Br. However, it includes all forms of Cl and Br and not just the ionically bonded ones tested by the IPC. Using the EN14582 test method, it is easy to test for all forms of Cl and Br.
Therefore, a material that is halide-free per the IPC J-STD-004 may not actually be halogen-free. The halogen-free definition is much more stringent.