We detail observations of gamma rays produced by interactions of cosmic rays and solar-energetic particles on the Earth's atmosphere. The Solar Maximum Mission (SMM) spectrometer accumulated the quiescent atmospheric spectrum over its full 9-year lifetime and our analysis revealed 20 resolved line features. We compare this spectrum with one collected on October 20, 1989, when SMM observed gamma rays produced by shock-accelerated protons that impacted the atmosphere in the polar region following an intense solar flare and coronal mass ejection. Observed nuclear-line intensities increased by over a factor of 50 during this event. Because this event was on the horizon and subtended a limited solid angle as viewed from SMM, the local increase was several times higher. We compare the gamma ray line energies, widths, and intensities from the solar event and quiescent atmospheric spectra and discuss their identifications. From this comparison we confirm direct observations that the solar proton spectrum is considerably softer than the spectrum of cosmic rays. Extension of an existing code for calculating solar gamma ray lines will provide information on the spectra of the protons reaching the Earth's atmosphere and thus on their transport through the magnetosphere. Broad spectral features found in the spectra are likely to be caused by a multitude of unresolved lines excited by neutron capture in the instrument, spacecraft, and Earth's atmosphere.