EUV emission-line intensities from the HRTS experiment on Spacelab 2 are analyzed to determine the causes of intensity variations from point to point on the solar surface. Chromospheric lines of O I and transition region lines of C II, Si IV, and C IV exhibit saturation effects that limit the line intensities in the brighter regions. No such effect is found in lines of C I, Fe II, or Si III. The chromospheric lines saturate because the optical thickness exceeds the thermalization depth, whereas the transition region lines saturate because of the geometry of the unresolved fine structure. The latter is assumed to consist of elongated cylinder-like features oriented along magnetic lines of force that are mainly vertical. Saturation occurs when the optical thickness along the axis of the cylinders exceeds unity. Estimates based on the observed saturation effects give fill factors for the fine structure of 5 x 10(-3) and 0.4 at 10(5) K and 3 x 10(4) K, respectively. The corresponding lengths of the cylinders are estimated at 1000 km and 40 km at the two temperatures. It is argued that in both chromospheric and transition region lines changes in density, temperature, and the volume of the emitting material each play important roles in the intensity changes from the one point to another on the solar disk. Evidence suggests that changes in the volume of the emitting material overshadow the effects of density and temperature changes. Intensity ratios of line pairs are shown to provide a reliable basis for density diagnostics if both lines are free from saturation effects and if they are formed at similar temperatures.