Comparing

A < B < a < b

Case Sensitive

This method is overloaded and is case sensitive by default.

System.String.Compare(sText1, sText2) 

sText1 < sText2

System.String.Compare("aaa", "bbb") = -1 (less than zero) 

sText1 > sText2

System.String.Compare("bbb", "aaa") = 1 (greater than zero) 

sText1 = sText2

System.String.Compare("aaa", "aaa") = 0 

sText1 <> sText2

System.String.Compare("aaa", "AAA") = 

Case InSensitive

It is possible to compare strings and ignore the case

System.String.Compare(sText1, sText2, True) 

sText1 = sText2

System.String.Compare("aaa", "AAA", True) = 0 

Testing For Equality

There are two ways you can test to see if two strings are equal.
You can use the Equals method from one of the strings

string sFirstName; 
string sLastName; 
bequal = sFirstName.Equals(sLastName) 

Or you can pass both the strings to the String class method.

string sFirstName; 
string sLastName; 
bequal = System.String.Equals(FirstName, sLastName)