What's the difference between the two UpdateSubject methods below? I felt using static methods is better if you just want to operate on the entities. In which situations should I go with non-static methods?

public class Subject
{
    public int Id {get; set;}
    public string Name { get; set; }

    public static bool UpdateSubject(Subject subject)
    {
        //Do something and return result
        return true;
    }
    public bool UpdateSubject()
    {
        //Do something on 'this' and return result
        return true;
    }
}

I know I will be getting many kicks from the community for this really annoying question but I could not stop myself asking it.

Does this become impractical when dealing with inheritance?