.NET SHA256 Vs Object.GetHashCode()

What are the pros/cons when it comes to using SHA256 Vs Object.GetHashCode()?

In the code below, the output is identical for both methods, however the GetHashCode() seems a lot simpler, requires fewer objects/code.

class Program
    {
        static void Main(string[] args)
        {
            TestGetHashCode();
            TestSha256();
            Console.Read();
        }

        static void TestSha256()
        {
            Console.WriteLine("Testing SHA256");
            UnicodeEncoding byteConverter = new UnicodeEncoding();
            SHA256 sha256 = SHA256.Create();
            string data = "A paragraph of text";
            byte[] hashA = sha256.ComputeHash(byteConverter.GetBytes(data));
            data = "A paragraph of changed text";
            byte[] hashB = sha256.ComputeHash(byteConverter.GetBytes(data));
            data = "A paragraph of text";
            byte[] hashC = sha256.ComputeHash(byteConverter.GetBytes(data));
            Console.WriteLine(hashA.SequenceEqual(hashB)); // Displays: false
            Console.WriteLine(hashA.SequenceEqual(hashC)); // Displays: true
        }

        static void TestGetHashCode()
        {
            Console.WriteLine("Testing Object.GetHashCode()");
            string data = "A paragraph of text";
            int hashA = data.GetHashCode();
            data = "A paragraph of changed text";
            int hashB = data.GetHashCode();
            data = "A paragraph of text";
            int hashC = data.GetHashCode();
            Console.WriteLine(hashA.Equals(hashB)); // Displays: false
            Console.WriteLine(hashA.Equals(hashC)); // Displays: true
        }
    }