No. A PWA has exactly the same storage access, code etc as a normal web page. A PWA is set apart by having a manifest, which defines how it should act as an app. It has certain extra capabilities like accepting shares and so on, but it is not radically different from a web page.
That is saying it uses a different storage area for the same thing and you presumably end up with different service workers between web and the app. Is that a good thing? My guess is they had no other choice.
Every browser other then Safari has the same storage for both PWA and website. Apple claims separate storage is "great for privacy" -- forcing you to use the cloud to sync between the PWA and the website.
