To get intrinsic adhesion or healing properties in a cross-linked rubber, two levers are possible: the inherent relaxation in permanently but lightly cross-linked elastomers or the relaxation due to exchange reactions as recently reported in the case of vitrimers. The former is associated with dangling chain motion and cannot be controlled. Lightly cross-linked rubbers may show interesting adhesion and healing properties, but at the expense of mechanical properties: ultimate properties are limited, and materials are subjected to creep even at low temperature. Conversely, exchange reactions may be triggered by temperature, providing the healable materials with strong elastomeric properties in a wide temperature range. Here a model system based on epoxidized natural rubber is presented which enables to differentiate and quantify the part of each process. A comparative study including stress relaxation, swelling experiments, and adhesion measurements highlights the advantages of the vitrimer chemistry on inherent relaxation as a proof of concept.