Subscriptions vs Memberships?

With the recent updates, I now see “members”, under their user info, have “Memberships” and “subscriptions”. Please help clarify the difference, and how the two interact, because I believe it’s causing issues in our system.

To note, we use the terms “subscription” and “subscribers”, even prior to the update. Just so I hopefully don’t sound like I’m confusing terms. We also use an org based subscription structure, seems to be another pain point.

We just had another subscriber renew – she renewed under a level that is/was not her current one. While working through how to best correct this, I see that she now has an error message and missing data.

Under “memberships”, it shows her old level, but for the subscription column, still under the “memberships” heading, it shows no subscription found.

Under the “subscriptions” heading, it shows her “new” level, but under the level description is says “membership ended”. ???

Through some more clicking around through the tables, I eventually end up at the “Orders” page, and click on the live link in the Transaction ID column, where i get the information you can see in the screenshot, with the error “This user does not have the membership level that this subscription is for”.

Which do I fix? How do I reconcile all of this, both here and database wide?

The page I need help with: [log in to see the link]