I saw this question asked on Reddit some time ago, and the answers were predictably passionate. For some people an audio drama is specifically a dramatic presentation in audio that includes sound effects and dialogue, nothing else. No narrator. No descriptive elements. Just the audio doing all the work. For others, as long as a story was being told in audio format, it is an audio drama. This includes things like audiobooks. I have to admit that I embrace this broader definition.
If an audio drama is simply a narrative told in audio, then we are embracing a heritage that goes back to the oral tradition and ancient tales like Beowulf or The Odyssey, which were originally told around campfires by a single performer, who included copious narration. But it also includes thirties era audio dramas like The Shadow.
In this way, I think there is one broad genre that is audio drama, and within that there are various versions of audio drama. This can include audiobooks (and even audiobooks have different versions, from full cast to duet to single narrator), “traditional” audiodramas that are nothing but sound effects and dialogue, and more narrative “oral tradition” audio dramas. This isn’t even a complete list, but you get the idea.
In short, in my opinion, if a story is told only using audio, then it is an audio drama.