What installing actually changes
An installed app and a web page can run identical code. What differs is where the icon lives, how much the device lets it store, which permissions it can request, and whether a third party can remove it from your device. Only the fourth is irreversible.
The words app and site suggest different technologies. Increasingly they are the same technology with a different wrapper, and the differences that remain are worth knowing individually.
The icon is the real feature
An app on the home screen gets opened; a bookmark in a browser does not. This is the largest practical difference and it has nothing to do with capability. Most of what installing buys, for most products, is that single change in how often you reach for it.
Storage limits differ
A browser gives a page a modest storage allowance and can clear it when space is short. An installed app usually gets more and keeps it. For a chat this matters only if conversations are stored on the device, which is a design decision rather than a property of installing.
Installing requests permissions; it does not grant them
Installing does not hand over the camera, the microphone or the contacts. Each is still requested when first needed and can be refused. The difference is that an installed app is allowed to ask for more kinds of permission than a page is.
Somebody else can remove it
An app from a store exists at the store's discretion, and it has been removed from devices retroactively. A page cannot be removed from your device by a third party, because it was never on it. This is the only difference on the list that you cannot undo.
Questions about the app
Is an installed app faster?
Marginally at start-up, because some files are already local. During use the speed comes from the network and the servers, and installing changes neither.
Does installing mean it works offline?
Only for what does not need a server. A chat needs a model, so the useful part stays online whatever the icon suggests.
Is a web app less secure?
It runs in a stricter sandbox, so in several respects it is safer. It also gets fewer capabilities, which is the same fact seen from the other side.
Add this to your home screen and compare it with the tab.
Open the chat first