yes, there is, as follows.
Unvulcanized rubber will soften and turn into taffy when it gets warm. Vulcanization cross-links the polymer strands and prevents the rubber from turning into taffy at high temperatures.
This also necessarily makes the rubber stiffer and more resistant to deformation at lower temperatures, which can yield a rubber compound which is not soft enough for a particular application. This tendency can be counteracted by milling mineral oils (plasticizers) into the rubber to get the rubber molecules to slip more easily past one another (within the limits set by the cross-linking).
This means that the process of engineering a rubber batch to have the right combination of flexibility and durability involves balancing the benefit of cross-linking against the need for rubber-like behavior, and this involves careful blending of plasticizers into the rubber resin. In so doing, the engineer can get anything from supersoft to almost rock-hard rubber, dialed-in for a broad range of special applications.