Difference between Equals/equals and == operator?

Question

What is the difference between a == b and a.Equals(b)?

Answer 1

String a = "toto".Substring(0, 4);
String b = "toto";
Object aAsObj = a;
Assert.IsTrue(a.Equals(b));
Assert.IsTrue(a == b);
Assert.IsFalse(aAsObj == b);
Assert.IsTrue(aAsObj.Equals(b));

This test pass in .NET, the trick is that Equals is a method, whereas == is a static method, so aAsObj == b use

static bool Object.operator==(object a, object b) //Reference comparison

whereas a == b use

static bool String.operator==(string a, string b) //String comparison

but a.Equals(b) or aAsObj.Equals(b) always use :

bool String.Equals(Object obj) //String comparison