That is at some level a distinction without a difference (and I have implemented PWAs, and tried to get them to work on mobile, including offline for significant periods of time). I've found (as a user) that most webview based apps (including those in the mobile stores) that I've used as a user tend to be held together with bits of string, and that running them in an actual browser tends to work better except in the case where there's literally no internet (i.e. for flaky internet browser beats wrapped pwa).