Outlook.live.com not syncing with Outlook 365. Suspect 2 different servers for same email address.

Having issues for several months that when closing Outlook 365 Windows progam (from Outlook 365 subscription) the program hangs intermittently. I rarely use Outlook.live.com, but have noticed my account is not syncing with the windows version of Outlook 365. 

It appears there are 2 different email servers with the same email name "g***@msn.com" one using MSN "Exchange" (The Windows Outlook 365) and one using Microsoft Office 365 (the Outlook.live.com). How do I resolve this issue? should I remove the Exchange account on Outlook 365 Windows and use the Microsoft 365 account instead? If so, how do I migrate the Exchange emails to 365 account.

Thanks for your help.