The term you're looking for is "Case sensitivity". This can be accomplished in MySQL using collation or in C# using the StringInstance.Equals
method with it's optional StringComparison
parameter. Usually programming languages are case-sensitive in string comparisons and database query languages are case insensitive (more properly, default collation is case-insensitive) so this can be quite confusing.
If you want to do this in the SQL Query itself, you'll want to collate the string in your query.
Example:
SELECT * FROM table WHERE Password = 'PassWord' COLLATE utf8_bin
See related SO question (in PHP, but still using MySQL)
If you are generating the query from, say, EntityFramework, you will want to want to use an somestring.Equals(someOtherString) method with StringComparsion.Ordinal.
Example:
MyObject obj = someQueryable.FirstOrDefault(q => q.Password.Equals("PassWord", StringComparison.Ordinal));
This will cause the generated query to contain the proper collation code.