Depending on your GPO or other settings you may not see all of your email as it is not caching them all locally. When you go office.com online you see all the email in your inbox and sent items.
What you can do to get more email cached locally is to change your default account settings by opening Outlook.
Select ” Account Settings”
on the “Email” tab Highlight your Office 365 Exchange account and select “Change”
You can then revise the “Offline Settings” Cached offline settings by moving the slider as shown below: