To test if the string paragraph contains the string word (thanks @QuarterMeister)

culture.CompareInfo.IndexOf(paragraph, word, CompareOptions.IgnoreCase) >= 0

Where culture is the instance of CultureInfo describing the language that the text is written in.

This solution is transparent about the definition of case-insensitivity, which is language dependent. For example, the English language uses the characters I and i for the upper and lower case versions of the ninth letter, whereas the Turkish language uses these characters for the eleventh and twelfth letters of its 29 letter-long alphabet. The Turkish upper case version of ‘i’ is the unfamiliar character ‘İ’.

Thus the strings tin and TIN are the same word in English, but different words in Turkish. As I understand, one means ‘spirit’ and the other is an onomatopoeia word. (Turks, please correct me if I’m wrong, or suggest a better example)

To summarise, you can only answer the question ‘are these two strings the same but in different cases’ if you know what language the text is in. If you don’t know, you’ll have to take a punt. Given English’s hegemony in software, you should probably resort to CultureInfo.InvariantCulture, because it will be wrong in familiar ways.