This research explores the surface properties of ten Centaurs through their reflective properties in the 0.6-5.3 μm range obtained using the JWST/NIRSpec spectrograph in the framework of two different programs: the JWST GO-1 large program "Discovering the Surface Composition of the trans-Neptunian Objects, Icy Embryos for Planet Formation" (DiSCo-TNOs; PID 2418) and the first Cycle One programs of Guaranteed Time "Kuiper Belt Science with JWST" (PIDs 1272 and 1273).Our study includes 52872 Okyrhoe, 3253226 Thereus, 136204, 250112, 310071 (Licandro et al. 2024), 10199 Chariklo, 55576 Amycus, 281371, and 459865 (Licandro et al, in preparation), and 2060 Chiron (Pinilla-Alonso et al., in preparation). We observe considerable diversity in their surface composition. Our analysis reveals two main categories among these bodies that mirrors similar findings in the Trans-Neptunian Objects (TNOs): those with surfaces composed of refractory materials plus some degree of water ice, and those with a higher content of carbon-based materials. Centaurs also include objects with a surface largely composed of refractory materials and little or no volatiles. As Centaurs travel closer to the Sun their surfaces tend to become less icy and more dominated by non-volatile materials due to the sublimation of volatile substances such as ice. Our compositional analysis suggests these Centaurs have a high concentration of amorphous silicates, indicating surfaces composed of primitive, comet-like dust. These findings suggest that similar groups in the solar system - including comets, Jupiter Trojans, Main Belt Comets, and D-type asteroids - which are initially thought to have had icy compositions, may undergo comparable surface changes due to thermal processing. Finally, our data strongly suggest that the color bimodal visible color distribution of the Centaur population is due to their original composition ('nature') and not to surface evolution ('nurture') as in the case of TNOs (Pinilla et al., submitted).