How to make the autocomplete term widget (tagging) case-sensitive?
You are looking for Termcase module, It will do that.


  It prevents users to use different cases on terms. With termcase you
  can make sure all terms in a vocabulary begin with an uppercase or
  that they are all formatted to lowercase.




There are five options available:


No formatting
Ucfirst: convert the first character of the term to uppercase
Lowercase: convert all characters of the term to lowercase
Uppercase: convert all characters of the term to uppercase
Propercase: convert the first character of earch word to uppercase


You can define these settings per vocabulary. The module even enables you to update all existing terms in a vocabulary and select whether or not you want to convert synonyms as well.