Have you double checked which Table each layout is showing records from?
It sounds like this is the culprit. it also sounds like you want both of your layouts to show records from Table B.
Think Table Occurrence, rather than Table. Each Table Occurrence is a box in Manage | Database | Relationships and you can have more than one Table Occurrence Box for the same table. In Layout Setup | Show Records From, you can see which table occurrence is selected for each layout. I predict that you will see different names here when you check each layout.
If you have different table occurrences of the same table and base a layout on each, you'll find that you have independent found sets, sort orders and current records on each and this would match what you describe here. If both layouts refer to the same table occurrence, then they'll share the same found set etc.
Turns out it wasn't a bug but a feature. I found out they were supposed to act independently and I wasn't using them as intended. And at the last minute, too--It's my departing employee's last day! That's what I get for not knowing how my staff use their systems.
Going into Edit Layout > Set Layout Order I was able to view a summary of which table was associated with each layout (as suggested by the other users), and comparing with an old database I was able to find where the settings needed to be.
Thanks for the help!