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We do see spectral lines in the Sun's spectrum, but paradoxically they
are absorption lines, not emission lines like we see in the neon sign.
Outside the photosphere there is a layer of cooler gas called the
"chromosphere". Gas in this layer, which is optically thin at most
wavelengths, absorbs light of wavelengths corresponding to spectral
lines of the elements present, and the Sun's spectrum looks like that
of an incandescent continuous source which is interrupted by missing
wavelengths. These lines are called "Fraunhofer lines" after the man
who discovered them (about 1830, I think). Similar features exist in
the spectra of stars. They are quite helpful in revealing to us
characteristics of the stars themselves.
Leigh