How have I got two identical Amazon Prime Video apps on my phone?
I can answer this one for you. Amazon are trying to transfer everybody to a new app. The one you linked to is the old one. Search the app store and you'll find the new one (at V6.4 vs 6.1 for the old).
A while back Amazon sent a push message with a link telling everyone to update. You probably did and didn't delete the old one.
What the difference is at this point in time between the two? Probably nothing. That might change though.