This is what I want to know
1. For an App to run on any iOS device it has to be signed.
2. There are two types of apps. "Private" apps and "public" apps.
Public apps are ones on the AppStore that follow all of Apples guidelines and are signed by Apple. This means that the iOS device recognizes that Apple allows the app to run on the device.
Private apps, or internal apps, are ones that are commonly developed and used by an organization. For example the US military has their own "AppStore" where you can install internal apps that they use. There are many companies that develop and send out internal apps that employees use. And these apps are signed by an enterprise developer license. so the app is allowed to run as long as the user, you, approves the app to run.
Because enterprise signature allows an app to run without going through the AppStore process this means that the developer doesn't necessarily have to follow the guidelines Apple sets for apps.
So a lot of times these companies will develop apps that don't follow the guidelines, sign them with an enterprise license, and put them online you anyone to download. Which installs a profile on the device that you have to trust before you can use the app.
That kind of app profile is not the same as MDM or other profiles. The app profile is there because it isn't a "approved by apple" app. The profile can't change settings, view any data about the device, and has no control over the device. However because the app is not approved by Apple the app may have spying code in it, and could act in a way that is unexpected.
I know it's long but I wanted to try to be as clear as possible.