For anyone interested, I have a 365 account and already had office installed on my machine, but just to see if there were any differences I downloaded Word a few minutes ago. As far as I can tell, it is exactly the same in look and function as what you could download from their website. I have the 2019 versions of everything.
I don't know that there is any reason for existing users to go through the app store, but it will definitely be nice for people downloading office for the first time or on a new device.
Did you Uninstalled web version first? or just installed over the web version?