Is the only difference in coil overs spring rate (which is almost always kept secret?)

Specifically speaking, H&R (street) has different model numbers depending on car model. Cooper, Cooper S, and Cabrio each have their own models (nothing listed for Cabrio S). What difference would it make, and could there be any problems?

I have came across a set for a good price. However, the model number matches that for a Cabrio(according to H&R site), but I have an S. should I keep looking?

 

TBH the cabrio weights more so maybe that's why there is a specific coilover for it, the same could be said for non-S coopers, they weight less than a S so the spring rate might be different to match this, I don't think the actual shock changes but I'm not sure about that either.