It has been posited that lunar eclipse observations may help predict the in-transit signature of Earth-like extrasolar planets. However, a comparative analysis of the two phenomena addressing in detail the transport of stellar light through the planet's atmosphere has not yet been presented. Here, we proceed with the investigation of both phenomena by making use of a common formulation. Our starting point is a set of previously unpublished near-infrared spectra collected at various phases during the 2008 August lunar eclipse. We then take the formulation to the limit of an infinitely distant observer in order to investigate the in-transit signature of the Earth-Sun system as being observed from outside our solar system. The refraction bending of sunlight rays that pass through Earth's atmosphere is a critical factor in the illumination of the eclipsed Moon. Likewise, refraction will have an impact on the in-transit transmission spectrum for specific planet-star systems depending on the refractive properties of the planet's atmosphere, the stellar size, and the planet's orbital distance. For the Earth-Sun system, at mid-transit, refraction prevents the remote observer's access to the lower ~12-14 km of the atmosphere and, thus, also to the bulk of the spectroscopically active atmospheric gases. We demonstrate that the effective optical radius of the Earth in-transit is modulated by refraction and varies by ~12 km from mid-transit to internal contact. The refractive nature of atmospheres, a property which is rarely accounted for in published investigations, will pose additional challenges to the characterization of Earth-like extrasolar planets. Refraction may have a lesser impact for Earth-like extrasolar planets within the habitable zone of some M-type stars.