In this paper, we show that a continuous-wave ytterbium-doped fiber laser implemented in the conventional configuration of a Fabry-Perot cavity with two fiber Bragg gratings as selective reflectors and a moderate output power (tens of watts) generates two groups of photons, each of which is characterized by its own statistics. The statistics of the first group are described by the M􀀀 fold degenerate Bose-Einstein distribution, where M is the number of independent states of spontaneous emission, which, in turn, depends on the laser linewidth and the radiofrequency band of the recording equipment. This kind of light is classified as narrow-band thermal light. The second group of photons is described by the extreme-value exponential statistics with a probability of encountering extremely large photon events much greater than expected from the Bose-Einstein distribution, which is classified as optical rogue waves. At a low laser power, the first group of photons strongly dominates over the second. As the laser power increases, the fraction of photons of the second group increases monotonically; above a certain threshold, the fraction of this group increases, reaching tens of percent of the total number of laser photons.