Hydrogen's confusing purple glow
The radiation of hydrogen in plasma with low density comes from discrete energy levels, resulting in spectral lines. Those spectral lines can be observed in sunlight, too. 

But the sun consists of a plasma with a much higher density. Most photons are the result of a long series of energy exchange inside the sun following the emission of high energy photons and kinetic energy of the nuclear processes. They are part of a continous spectrum as there is not a discrete number of energy levels at the interactions in this high density plasma.

In the photosphere, some of them are absorbed again and result in negative spectral lines (Fraunhofer lines), but the main portion of light remains a continuous spectrum.