If you select Code Display (or Hex Display) on both String indicators you will immediately (or not) see the difference.
The MD5 function returns "0D" character which is interpreted as "\r" - carriage return.
When you save that character to file it is changed to "0A" ("\n") - new line.
If you want to save MD5 to a text file first you would need to convert text to ASCII numbers and then save those numbers as text.
This way you will avoid automatic conversion of special characters.
Do you see the little square with the arrows in it on the lower right corner of your read and write text VIs? Those boxes inform you that the VIs are converting EOLs. Right-click on each of them and deselect "Convert EOL" and you should be fine. I hope I got here soon enough that you didn't create some kind of Rube-ish code to compensate for the conversions...