Need to uninstall Office 2011 first?

With older Office versions, I remember MS saying to remove older versions before installing new ones. However, you should check with the developer to be sure.

Not sure where it is in Office 2011 but v2008 had an uninstaller in the main Office folder in Applications:

Does a nice job.

There are two versions of Office available, Office 2019 a one time purchase, and, Office 365, a subscription license.

Questions about Microsoft licensing, versions, and installation can be asked in the Microsoft product Help Communities: https://answers.microsoft.com/en-us

Either Office 365 (Mac App Store applications) or Office 2019 for Mac provide their own applications that reside on the Mac. You will need a new subscription/license for either. Each application is self-contained, including fonts.

I believe that Office 2011 for Mac can be co-resident with the new applications, though having not received any updates since Oct 2017 when it was retired by Microsoft, I have my doubts that Office 2011 for Mac will remain compatible with Mojave. Certainly no fixes coming if something breaks in it.

They can both be on the drive, though there isn't much reason to have 2011 once 365 or 2019 is installed.

For whatever reason, MS did not include an uninstaller for 2011. It all has to be removed manually. Microsoft's site says to simply put the main folder of apps in the trash. That leaves a lot of smaller junk behind. Much more thorough instructions here:

https://www.howtogeek.com/212650/how-to-completely-uninstall-office-2011-for-mac/

Be careful on the last step, Moving or Deleting Your Microsoft User Data. DO NOT delete the Main Identity folder until you have imported your Outlook 2011 data into the 2019 or 365 version. Once the import is done, then you can delete it as Outlook 365/2019 will never look at the Main Identity folder again. The new location for Outlook's data will be:

/Users/your-home-account/Library/Group Containers/UBF8T346G9.Office

Doesn't matter what order you do it in. Just make sure to keep the Main Identity folder until after the data has been imported into Outlook 365/2019.

It is both, you can either use it web-based or installed on your computer.