From their brief summary descriptions, it sounds like the string comparison rules StringComparison.Ordinal and StringComparison.InvariantCulture ar
StringComparison.Ordinal
StringComparison.InvariantCulture
It does matter, for example - there is a thing called character expansion
var s1 = "Strasse"; var s2 = "Straße"; s1.Equals(s2, StringComparison.Ordinal); // false s1.Equals(s2, StringComparison.InvariantCulture); // true
With InvariantCulture the ß character gets expanded to ss.
InvariantCulture
ß
ss