What is the Factory Method pattern, and how does it differ from the simpler Static Factory Method idiom (like List.of() or Optional.of())?

The Factory Method design pattern (Gang of Four) defines an abstract method in a base class that subclasses override to determine which concrete type gets instantiated, deferring instantiation decisions to subclasses as part of a broader class hierarchy design; the more commonly used "static factory method" idiom (a simpler, unrelated convention popularized by Effective Java) is just a static method on a class that returns an instance of that class or a related type (like List.of() or Optional.of()), used primarily for more descriptive naming than a constructor, controlling instance caching/reuse, or returning a subtype without exposing it -- despite the similar name, these are genuinely distinct concepts serving different structural purposes.

// GoF Factory Method pattern: subclasses decide the concrete type
abstract class DocumentCreator {
    abstract Document createDocument();  // subclasses override to return different Document types
}
class PdfCreator extends DocumentCreator {
    Document createDocument() { return new PdfDocument(); }
}

// Static factory method idiom: just a descriptively-named static creation method
public class Point {
    public static Point of(int x, int y) { return new Point(x, y); }  // more readable than 'new Point(x, y)'
}