Well it appears that you have a case insensitive collation, so CHECKSUM won't show a difference between the same word with different cased letters. Just as if you did it in SQL; 'test' = 'TEST'.

If you need to make that sort of update there are several options. One option is to COLLATE your strings to something Case Sensitive before applying the CHECKSUM function. Another option is to use the BINARY_CHECKSUM function (updating your checksum columns type appropriately). There are other options, but those are probably the easiest.