Intrinsic differences between tunneling two-level systems (TLSs) in molecular versus polymeric glasses are revealed by studying the effect of compression on TLS dynamics. Photon echo studies under variable low-temperature (1.1-2.3 K) and high-pressure (0-30 kbar) conditions have been performed to contrast the effect of compression on molecular [2-methyl-tetrahydrofuran (2MTHF)] versus polymer [Polymethylmethacrylate (PMMA)] glasses. The pressure-induced reduction in the magnitude of the optical dephasing rate of rhodamine 640 in a molecular glass (2MTHF) is found to be comparable to the volume decrease of the glass (e.g., approximately 20% at 30 kbar), indicating that TLSs in 2MTHF are associated with void space or low-density regions of the glass. In contrast, the relative pressure insensitivity observed for organic polymer glasses (PMMA) supports the idea that these TLSs are associated with side chain defects. The power-law exponent for the temperature-dependent dephasing in 2MTHF also decreased significantly at high pressure, suggesting a change in the form of the TLS density of states upon compression of the molecular glass.