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One of the most fundamental quantum random number generators is implemented with light impinging onto a beam splitter, and two single photon detectors at its output. Often, this generator is described as 'a photon which takes one or other path towards a detector'. The input state of light in conjunction with the detector response is relevant for the amount, the pattern, and the correlation of the generated clicks. Only a fraction of all generator outcomes, the min-entropy, can be used as a further resource for true randomness. This paper addresses the difference in the common description with incoming single photons and the often implemented scheme with a weak coherent light source, such as an attenuated laser. For this very fundamental and widely used configuration the amount of usable entropy is compared. If single photons from an anti-bunched light source are supplied, the amount of entropy is higher than for the case of a supplied coherent state - although the latter can be arbitrarily bright unlike the single photon source. [ABSTRACT FROM AUTHOR]