In the Edge browser there is a browser process running in the same appcontainer defined by its appx manifest, but there are also tab processes. These tab processes are running in restricted app containers that have fewer appx capabilities. The browser process has XAML loaded and coordinates between tabs and handles some (non-WinRT) brokering from the tab processes. The tab processes load edgehtml and that is where they render HTML, talk to the network and execute script.
The ApplicationContentUriRules (ACUR) section of the appx manifest lets an application define what URIs are considered app code. See a previous post for the list of ACUR effects.
Notably app code is able to access WinRT APIs. Because of this, DOM security restrictions are loosended to match what is possible with WinRT.
Privileged DOM APIs like geolocation, camera, mic etc require a user prompt in the browser before use. App code does not show the same browser prompt. There still may be an OS prompt – the same prompt that applies to any UWP app, but that’s usually per app not per origin.
App code also gets to use XMLHttpRequest or fetch to access cross origin content. Because UWP apps have separate state, cross origin here might not mean much to an attacker unless your app also has the user login to Facebook or some other interesting cross origin target.
On the web a subset of web sites are web apps. These are web sites that have app like behavior - that is a user might call it an app like Outlook, Maps or Gmail. And they may also have a W3C app manifest.
A subset of web apps are progressive web apps. Progressive web apps are web apps that have a W3C app manifest and a service worker. Various OSes are beginning to support PWAs as first class apps on their platform. This is true for Win10 as well in which PWAs are run as a WWA.
Within that we have a notion of a packaged web app and an HWA (hosted web app). There's no real technical distinction for the end developer between these two. The only real difference is whether the StartPage identifies remote HTML content on the web (HWA), or packaged HTML content from the app's appx package (packaged web app). An end developer may create an app that is a mix of these as well, with HTML content in the package and HTML content from the web. These terms are more like ends on a continuum and identifying two different developer scenarios since the underlying technical aspect is pretty much identical.