While I do not claim to know exactly why they differ, I will offer some advice.
It is not good practice to use either server name or IP when referencing PWA, nor is it preferred to use AAM's.
Best practice is to use a friendly URL registered in DNS for your SharePoint web application upon creation.
The reason is that during provisioning PWA will use the "Default" Zone when building out the internal bits which includes the contents of the BI Center (the ODC Files for example).
so that may be part of the answer to your question - whatever is set as the default zone (server name?) will be the "correct" URL that PWA knows about.
So while AAM's may be good for SharePoint in general, they are not ideal for PWA and his content.
I would recommend to rebuild your SharePoint web app on the new URL and then re-provision PWA on that web app (meaning the default zone has the host header URL).
all should well then.
Hope that helps
Thanks, Eric S. Pcubed
PS Re-reading your OP, you are using PS 2016, as the URL for 2013 is /ProjectBICenter, is that right?
And you may have just stumbled on some additional pages that MS left in the directory.