Hi Sbond,
Thanks for the screenshot. When you say "I would like the view in Outlook 365", do you mean Outlook 365 desktop client or Outlook Web App on Office 365?
Regarding "I am used to in the desktop version", do you mean that Outlook 2016 desktop client version or else?
I have checked on my side using Outlook 2016 can see the same as you posted screenshot group by Date (Date: Today, Date: Last Week, Date: Two Weeks Ago).

However, using Outlook 365 desktopclient version 2102 Build 13801.20360 I can't do that group by Date (e.g. Date: Today), see screenshot below.

Note: Also using Outlook Web App on Office 365, it's not feasible to do group by Date as you mentioned.
If I have misunderstood anything please correct me and provide us with detailed information screenshot about Outlook 365 version (see About Office: What version of Office am I using?) so that we can further assist you.
Your patience is highly appreciated. Have a nice day and stay safe!
Best regards,
Shyamal