It can be minimal, it can be significant difference, all depends on the PWA implementation.
Installed app has a shortcut/desktop icon, which is good for return engagement. A flash screen ratehr than the blunt loading of a web page. The UI can be instantly there as well as some content using offline tactics. A PWA isn't compromised by all kinds of browser real estate.
A proper PWA can definitely be better or approach a proper desktop app, but it's true that few implement them in that rich way.
Secondly, not having Electron all over the place.
Firefox is also my main browser, but that doesn't change the fact that its 3% market share has made it optional for project delivery acceptance testing.
I hardly see it in any browser matrix nowadays.
"Why do I need a screenshot of the "app" (i.e. webpage) I am already using?"
Said pop-up is related to increasing Web apps adoption.
You're on a Web site. It has an "Install" button that you can click. Following the change announced in this post, the popup that overlays the page content can now contain a screenshot of the site operator's choosing when Chrome prompts you to confirm installation—a screenshot that could just as easily appear on the page—i.e. the one that you are already on and that contains the install button you just clicked. The question, then, is: ignoring all the puffery and filler the blog post, what _actual_ problem does this (the "screenshots" property—and not a PWA in general) actually solve?
(Alternatively, you can say something like how you were so excited when it seemed like there was an opportunity to post a vaguely cynical and nearly zero-effort quip related to installable Web apps vs Electron that you came in firing from the hip which resulted in what, as it turns out, was a response to a different question that nobody here was actually asking. It's as simple as saying, "Oops. I was mixed up, and I don't have such a big ego that I can't admit this nor one that requires me to pretend that this is what I meant by my original comment in this thread all along.")
This is one of the primary reasons why many developers still prefer to publish in App Stores, despite the various obstacles and risks involved.
Mobile Safari also treats websites differently if users add them to their home screen. It doesn't aggressively remove local storage in these cases. However, I am not certain about Chrome's behavior in this regard.
When the person you are responding to writes, "What user problem is being solved by this?" they are not being asked to have the value proposition of "installable" Web apps explained to them. They are asking about exactly what they say they are: "Why do I need a screenshot of the "app" (i.e. webpage) I am already using?"