The spectral diversity of trans-Neptunian objects (TNOs) is crucial for understanding the processes that led to the formation and evolution of planetesimals in the outer solar system. Using near-IR (NIR) spectra obtained by the James Webb Space Telescope (JWST) as part of the DiSCo-TNOs large program, we report the detection of well-clustered subgroups of TNOs. A first subgroup has strong NIR features with contributions from H2O, CO2, CO, CH3OH, and other organic molecules. The 2.27 μm band area, commonly attributed to methanol, decreases with increasing eccentricity, which is compatible with a late destruction of CH3OH by cosmic ion irradiation at the edge of the heliosphere. The absence of the strongest CH3OH bands in the JWST spectra is compatible with an irradiation-induced surface stratification, with CH3OH abundance increasing with increasing depth. A second subgroup has much weaker NIR bands, and these cannot be explained by a late irradiation scenario. This group is further divided into two subgroups (cold classical TNOs and objects with low perihelion) that are spectrally very similar except for their CO2 band area. We propose two possible interpretations. In one scenario, the TNO subgroups sampled a similar molecular inventory in the protoplanetary disk, after which early surface processes, such as primordial sublimation or irradiation from the young Sun, sculpted the two groups before planetary migration occurred. In a second scenario, the subgroups formed in different locations of the disk where molecules were available in different abundances. A combination of both scenarios is also possible.