How do I know on which devices I can use a purchased app?
It's not a question of licensing, it's that the architecture of the Mac &amp; an iDevice are totally different.

The Mac runs on an Intel processor, OS X is based on a unix kernel.

iDevices run on an ARM processor, iOS is [actually idk, but proprietary]
(All iDevices run on the same 'family' of processors, so that is why if you purchase an iApp, you can use it on any iDevice you own.)

Apps for one simply cannot run on the other.  

Some apps are made in 2 or more versions, for Mac, iPhone, iPad, even Windows or Android etc, each available from their respective Store.   

The App Store 'app' on the Mac is only for Mac Apps. iApps can be purchased either from the App Store on the iDevice, or through iTunes on a Mac/PC.

The licensing model for Apple is that the Apple ID used to purchase an app from the App Store is allowed to use it on any device they own using that Apple ID  [1] [so long as it will physically run, as explained above]
This makes moving from machine to machine easy, but not from ID to ID.
It's pretty much the opposite of the Microsoft model, where an app, or even the OS itself is tied to one machine, using a serial number etc.

 [1]with some exceptions which you can see noted in the Purchases tab in the App Store app.
An example…



Interestingly, the only apps I have that are not shareable are all Freeware anyway, so I could simply re-"purchase" if I needed them on another machine.

Family Sharing extends that licensing model to other members of your family, so all can access the same songs, albums, movies, TV shows, books, and apps on both Mac and iDevices, if they wish, from a single 'purchase'.