Jeez, I don't know
I mean it. I really don't know. There are so many ways to interpret that description that I can only tell you there is no standard.
Documentary Photography. Photojournalism. Candid Photography. Storytelling Photographer.
Throughout my career I've cycled through so many of these words. Some come into fashion and work for a while, but then their original meaning gets diluted as they catch on. More photographers start picking them up because they see the big names using them, the successful local shooters embracing them. Once they become marketing speak, they lose their clarity.
It's worth mentioning that a lot of photographers are not great at describing themselves in words. I include myself in that. We're visual people. We speak in images. We tell stories with light and composition the way writers tell them with sentences. Sometimes those stories are long narratives that rely on shared experience for the viewer to fill in the gaps. Sometimes they're more like a short poem, or a single witty one liner.
The bottom line is that there is no standard, and I don't think we should get too hung up on the labels. Instead, ask your photographer some probing questions about their philosophy and process:
How much do you direct your subjects?
What does that look like in practice?
Am I just supposed to go about my day while you work around me?
Those answers will tell you far more than whatever words they've chosen to put on their website.
I think of myself as a photographic storyteller, but even that doesn't tell the whole story. My subjects aren't required to perform for the camera while I lurk in the shadows waiting for something to happen. I'll direct you when the moment calls for it. I won't interrupt when the moment is sacred. I've learned to trust my experience and my gut to know the difference. A day with me will have many different kinds of moments in it. There are directed portraits where my whole intention is to make you look beautiful, happy, and completely loved. There are also quiter moments I simply had the instinct to catch. Both are real. Both are part of the story.
That's what I mean when I say documentary. But please ask me anyway. I'd rather show you than try explain it in words.