An additional difference to the ones listed in the excellent accepted answer is that (since C# 7.0), is between two NaN values is a pattern that matches, because x.Equals(y) is true when both x and y are NaN, and a NaN value does not have an integral type. Therefore, is not between two NaN values returns that the pattern is not a match.

However, C# follows IEEE floating-point and C by specifying that a != comparison between two NaN values is true and an == comparison between them is false. This was mainly because the Intel 8087 floating-point co-processor back in 1980 had no other way to test for NaN.

Nan and null are properties that variables can contain that have no values. Equality checks require an actual value to determine equality. After all the question on whether Sally and Peter has the same amount of apples when nobody knows how many Apples either of them has is meaningless.

Sometimes you want to check if a variable has a property without a value. A basic equality check would not be sufficient for this. That is when is / is not operator is useful. It could be said != is a value check where is / is not a property check.