Convert is a class that contains a series of static methods and is suposed to be used to convert base types, the supported types are Boolean, Char, SByte, Byte, Int16, Int32, Int64, UInt16, UInt32, UInt64, Single, Double, Decimal, DateTime and String.
The cast operator allows you to do the same thing but you can use it for other types as well, including the types you create. You also can define this operators in your classes, allowing you to convert from anything to anything.
So thats the difference, one is a method and the other one is an operator, I have not checked the guts of the operaror when converting and int to a string, but it might have the same logic as the methods in Convert.