In order that a snapshot can have the quality of portrait, it must have something of the nature of caricature. Caricature is precisely the anti-snapshot, capturing something that is not simply momentary or even ephemeral, but characteristic: something that stays the same in different observations of a person's movements and gestures and facial expressions.
Yet, the singularity – the one that we strangely feel that we can observe – can be such that it can only be captured in a fleeting moment, drawn in a quick sketch or captured in a snapshot.
The object of our observation, the model herself, might not recognize the enduring nature of that observation, however. It might be alien to her own self-image or rather self-experience, even when everybody else, nous autres hommes, would confirm its vraisemblance.
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Exposure time might be the question.
A case in point, or perhaps an antitype (an exception to prove the rule, as outlined above), the famous daguerreotype of Edgar Allan Poe, by W.S. Hartshorn (1848):
Some pictures make caricatures futile.