Naturally created white light contains photons of every visible frequency, so you’re correct in thinking it’s the latter. The difference is that a beam of light is usually a LOT of photons, especially if it’s bright enough to see! (The lower limit for your eye’s sensitivity is generally about 100 photons per second.) By definition, your eye is only sensitive to the visible range of light, so to define “white” light as we see it, ignoring the rest is a fair thing to do.
Perhaps a better term would be a ‘stream’ of photons; the 'beam’ is usually referring to the fact that the light is focused to a very narrow region of space. Single photons are extremely difficult to isolate, and usually if you go to that effort, you’re trying to test quantum mechanics in some form.
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