Observations of the time-dependent, electron-positron annihilation line radiation and gamma-ray continuum emission from the region of the Galactic Center show that there are two components to the annihilation line emission: a variable, compact source at or near the Galactic Center, and a steady, diffuse interstellar distribution. We suggest that the annihilating positrons in the compact source, observed from 1977 through 1979, result from photon-photon pair production, most likely around an accreting black hole, and that the annihilating, interstellar positrons result from the decay of radionuclei produced by thermonuclear burning in supernovae.