I understand the process of electron transitions but I don't understand how or why these pictures are put together. If we're looking at the spectra of a star, why are this pictures shown as absorption spectra and not emission?
This is the spectrum of the light that actually comes from the star. We don't get to choose whether emission or absorption dominates - the physics of the star determines that. Most of the light from the star is continuous black-body radiation from the stellar plasma and not from atomic emission lines. The absorption lines remove some of this continuum spectrum.
The terminology can be confusing sometimes, indeed. The spectrum of a typical star is continuous, determined by the effective temperature of the photosphere of the star. However, there are absorption spectral lines superimposed on this continuum, because photons of some specific wavelengths are being absorbed as trying to escape through the stellar atmosphere. The absorption spectrum is determined by the composition of the atmosphere and by the level of ionization.
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