Whilst the terms flame retardant and fire retardant are often used interchangeably, the flame retardant is actually the correct phrase to be associated with the chemical treatment of fabrics and other materials in order to prevent or slow the further development of ignition when the material comes into contact with a source of ignition such as a flame.
By contrast, fire retardant relates to using substances to reduce the flammability, specifically of organic materials which may include fabrics, but also materials found in buildings and wildlife.