looks like this on both machines, yet they dont have the same tab or primary inbox,
It might be that you have Inbox categories configured on one but not the other, or different Inbox categories configured on both?
Which inbox category tabs do you see (Primary, Promotions, Social, Updates, Other…) above your message list on each computer?
You can choose which Inbox categories your incoming emails are sent to by right-clicking on any Inbox category tab or the space next to it and making a selection. After you have made a selection, existing Inbox emails will be moved accordingly.
If you prefer a single Inbox, you can disable categories altogether under Settings / Mail / Categories:
I don’t know if this helps or you have a different kind of issue?