Correct. But it does have full FDA approval. The vaccine does not. See the difference?
Lots of misunderstanding (or misinformation) about how this works, so let me try to clear things up:
Pharmaceutical companies and others who develop new drugs typically submit an IND (Investigational New Drug) to the FDA. These incorporate clinical protocols that test safety and efficacy, with strict requirements for Institutional Review Board review, informed consent, and other controls. The desired endpoint is FDA approval for a given medical indication or set of indications.
Under emergency situations such as the ongoing COVID-19 pandemic, the FDA may grant Emergency Use Authorization for a drug or other therapy. This requires safety and efficacy data as well, though possibly less than needed for full approval, depending on the nature of the emergency. EUAs expire when the emergency conditions are over. In the case of SARS-CoV-2 vaccines that have been granted EUA, the volume and rigor of supporting information was quite high. While it's possible that further study may produce different results, the volume of data gathered worldwide since EUA has been massive, and this hasn't happened.
Occasionally, the FDA may allow use of an investigational drug for expanded (also sometimes called compassionate) use. This can be done for an individual or group in life-threatening circumstances when there are no alternatives. I suspect this is what allowed Trump to receive monoclonal antibody therapy last year.
Finally, any approved drug may be used off-label — that is, to treat conditions for which it was not approved. This can be done at the discretion of the treating physician or other authorized healthcare provider.
I often hear claims that the vaccines are investigational or experimental and therefore not safe, while drugs like HCQ are because they're approved. But the quality and quantity of supporting data are what matter. Unfortunately, most people who take one position or another have no ability to assess the validity of scientific studies, so they parrot what they've heard or read in social and other media.