Site membership vs paid membership confusing our users

Question:
Site membership is making users think that they have joined our Association as a member, and can qualify for things like events that are only free to paying members. Is our only option to switch off site membership to avoid any confusion, thereby losing our member area?

Product:
Wix Studio Editor.

What are you trying to achieve:
We run events where our paid members (on a pricing plan) get free registration, whilst non-members have to pay. People who join our mailing list and become site members are choosing the member rate for our events, understandably thinking that they are now members of our association. Is our only option to turn off site membership, thereby deleting our member area? Similarly, site members appear in our directory when I want to restrict that to paying members only.

What have you already tried:
I can find information about how to turn off site membership, but we do want to keep a members area if we can (but exclusively for pricing plan members).