Remaining Balance will show the entire remaining balance (even if it's not 'Due') on any project status.
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Amount Owed will only show funds that are currently 'Due' or ‘Overdue’ on signed projects.

For example:
I have a project that's today for $100.00, and this project is on a Net 30 Payment Policy.
The Amount Owed column will show nothing is Owed, but $100.00 will show in Remaining Balance.

I have a project that's today for $100.00, and this project requires a 50% deposit that the client didn't pay.
The $50.00 will show in Amount Owed, and $100.00 will show in Remaining Balance.

In terms of reporting, Remaining Balance will answer the question "What can I stand to make?", whereas Amount Owed will answer the question "What is overdue that I need to collect?"