In POM (Page Object Model) you create new class for every new page/URL and put all your element identification methods in it.
If you navigate to my Github - OrangeHRM automation sample project, you will notice that I have two .java files there. Dashboard and Login. So whatever element I identify on Login page, I put in Login.java and whatever elements I identify on Dashboard, I put it in Dashboard.java. This is really helpful in terms of maintenance and usability. So, if I want to work with any element present on Dashboard, I just have to say Dashboard.element. If case of change of element, I just have to change it at one place.
Page Factory is annotation inside selenium which you give it to class. So, when you define any class as page factory, all your elements inside the class will get loaded while any of element in the class is called. This is really a bad practice if you have 100s elements inside a class and you just have to make use of only one.
So, I would suggest you to go with POM. I do not have C# example, but I have similar one in Java which I have already shared.
Feel free to comment back if you need more details.