It's important to know the difference between these two settings because they are both helpful in different ways. :)

For memberships that say "No expiration date, re-bills on ...":

This is only seen for members under a Membership type that is set up to automatically re-bill and have their Credit/Debit card information saved on file.
These memberships will automatically re-bill on their date listed in the Stripe column on the top left-hand side of your members account.
These memberships will receive Renewal Reminders (Type B) -- this is a general reminder of an upcoming payment with no action required.
If their payment fails multiple times, then they might be moved to 'inactive' state (this setting is found within Stripe - more information can be found here).

For memberships that say "Expiration Date: XYZ":

This would typically be seen under a One-time payment Membership type.
These memberships cannot be automatically re-bill because they don't have a credit/debit card saved in Stripe.
These memberships will receive Renewal Reminders (Type A) -- this email has a strong 'Call To Action' prompting the member to manually renew their membership.
If they don't renew their Membership by their 'Expiration Date', then they will be automatically moved to 'Expired'

Note: The system behaves differently depending on whether a Membership is already set to automatically re-bill. If a member is added to your database manually (via the dashboard, or a Bulk Import), then their credit card information will not be stored in the system -- So they'll have to manually renew when they reach their Expiration Date.