Does the hydration of a starter actually matter?

I generally keep my starter at 75% hydration, because I find it easiest to work with at that level. For most recipes which call for a specific hydration of the levain, I just adjust the hydration in the final dough accordingly. However, some recipes call for a drastically different hydration-- a real stiff starter, or a seriously liquid starter-- and for these, I have been actually making separate levains.

Is this necessary?

Let's say a recipe calls for a stiff starter at 40% hydration. If I adjust the final water amount in the dough, can I just use my 75% hydration starter? Or do stiff and liquid starters really develop different properties, which I would miss out on if I simply adjust the total water amount?

Thanks in advance for any guidance. If my question is not clear enough, please let me know.