InvariantCulture
Uses a "standard" set of character orderings (a,b,c, ... etc.). This is in contrast to some specific locales, which may sort characters in different orders ('a-with-acute' may be before or after 'a', depending on the locale, and so on).
Ordinal
On the other hand, looks purely at the values of the raw byte(s) that represent the character.
There's a great sample at http://msdn.microsoft.com/en-us/library/e6883c06.aspx that shows the results of the various StringComparison values. All the way at the end, it shows (excerpted):
StringComparison.InvariantCulture:
LATIN SMALL LETTER I (U+0069) is less than LATIN SMALL LETTER DOTLESS I (U+0131)
LATIN SMALL LETTER I (U+0069) is less than LATIN CAPITAL LETTER I (U+0049)
LATIN SMALL LETTER DOTLESS I (U+0131) is greater than LATIN CAPITAL LETTER I (U+0049)
StringComparison.Ordinal:
LATIN SMALL LETTER I (U+0069) is less than LATIN SMALL LETTER DOTLESS I (U+0131)
LATIN SMALL LETTER I (U+0069) is greater than LATIN CAPITAL LETTER I (U+0049)
LATIN SMALL LETTER DOTLESS I (U+0131) is greater than LATIN CAPITAL LETTER I (U+0049)
You can see that where InvariantCulture yields (U+0069, U+0049, U+00131), Ordinal yields (U+0049, U+0069, U+00131).
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