Installing an app creates an instance: the app plus your settings. The instance is what goes in a playlist, not the app itself.
One app can have as many instances as you need. The same weather app runs three times with three cities; the same dashboard app runs against three different reports.
Where they live
Your instances are listed under Apps, separate from the store you install them from, and they appear in your content library alongside everything else.
Search and the Recently added grouping both work on that list, which starts mattering around the point you have a dozen.
Editing one
Open the instance and change its settings. Everything showing it follows on the next sync, exactly like editing any other content.
Editing an instance changes it everywhere it is used. If two screens should show the same app configured differently, that is two instances, not one edited back and forth.
Different app, same idea
This is the same relationship content has with playlists. An instance is a thing in your library; the playlist references it. Deleting a playlist leaves the instance alone.
Removing one
Delete app removes the instance. It comes out of every playlist that used it, on every screen, on the next sync.
Deleting an instance does not uninstall anything from a device and does not affect other instances of the same app. It also does not touch the connected service it was reading from.