The expansion being performed was often incorrect, as it's possible for
the tilde character to appear as part of the path where it should not be
expanded to the user's home directory.
Properly supporting tilde expansion is complicated and requires
additional study. Instead of supporting it only partially, we have
decided to simplify things and just drop tilde expansion for now. See
the discussion in issue #2619, as well as issues #2325 and #2555.
InvariantCulture is useful when comparing / sorting human language strings in a culturely correct way. It handles things like accented letters in a way that makes sense to humans (e.g., 'a' should be sorted next to 'á', rather than after 'z').
Ordinal looks just at the raw code points of the characters. As such, it is recommended for use in cases when comparing system strings (file paths, command line parameters, config settings, etc.). Since it doesn't need to use the culture specific sorting rules, this method can often be faster.
For more information, see https://stackoverflow.com/questions/492799/difference-between-invariantculture-and-ordinal-string-comparison (and other related questions)