There are many definitions on the internet of what the factory pattern would/should be. It is important to comply with your professor while you study at a university. Besides that programming is an art. It has nothing to do with naming conventions. Mona Lisa could be named Paul, you see. Only posh people care about technique naming. But if you paint a picture yourself, you don’t care about any technique naming convention at all; you only care about your results. And if people like it, then you are successful. It is the same with programming.
The Factory Method Pattern usually refers to a class that creates just one type of object.
The Abstract Factory Pattern usually refers to a class that can create various types of objects, which have something in common.
Besides that we have a lot of gibberish about some 10 and more years old pattern.
I could add a lot of code here, but it should suffice to just get the idea of it. Have a look at the above picture. An abstract class/interface is used as the base class for country specific factories. These factories create the objects.
The Z4 Model is built in Germany and China (just for demonstration purposes). Basically they are the same besides the difference between the Chinese and German regulations.
Now, translate that to your own business case. You may need a Factory that creates code for your Unix, Mac, and Windows system. On top of that you may have to create two distinct objects for your test and prod environment.