Intersect vs IntersectWith in C#

Hello,

I understood how IntersectWith works but How does Interset work in C#?

using System;  
class TestsRethrow  
{  
    static void Main()  
    {  
        string[] Family = { "Harrison", "Joe", "Grace" };  
        string[] Friends = { "Jake", "Mary", "Joe" };  
  
        HashSet<string> duplicate = new(Friends);  
        HashSet<string> duplicateWith = new(Friends);  
  
        duplicate.Intersect(Family); // How it works?  
        duplicateWith.IntersectWith(Family);  
  
        Console.WriteLine($"Intersect {duplicate.Count}");  
  
        foreach (var item in duplicate)  
        {  
            Console.WriteLine(item);  
        }  
        Console.WriteLine("\n");  
        Console.WriteLine($"Intersect With {duplicateWith.Count}");  
        foreach (var item in duplicateWith)  
        {  
            Console.WriteLine(item);  
        }  
    }  
}