What material properties influence stretchiness? (Rubber/Silicone)

Assuming I want to create a product that is very stretchy - like a rubber band.

What do I have to tell the manufacturer regarding the material?

Do I just say it should have a Shore Hardness of 30-40A? Is that enough for the manufacturer to know what I mean? Or are there other properties that influence the stretchiness?

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Assuming the Shore Hardness is 30-40A - is the stretchiness the same between TPU/TPE/Silicone/Rubber/… etc. ? Or will there be differences?