Rehabilitation for drug or alcohol addiction is considered a short-term disability in that it is temporary and is an illness. Once your unique situation has been assessed, it will be determined what is covered under short-term disability and FMLA. If you are considering short-term leave and FMLA leave for it to be applicable, your employer may categorize one leave under a specific type and the other departure under a separate category to ensure that you get the help you need without having to worry.
If you are not covered under FMLA, your insurance policy may cover it. Short-term disability applies to most full-time employees if they meet the criteria and qualify. It's best to sit down with your employer and truly determine what is covered and what you are eligible for.