- An umlaut denotes a specific pronounciation. Common in German and Hungarian, u and ü for example, are two different characters and their use in a word can substantially change the meaning of the word if the ü were changed to u.
- The diaeresis is used over the second instance of a pair of vowels in some words. It denotes either a difference in emphasis or pronounciation (such as for double vowels in words like preëmptive, coöperation), or indicates that the second vowel, which might normally be silent, is instead pronounced (compare the ai in pain and naïve).
In English, it's more common to see the second usage of the diaeresis (naïve) than the first although some publications, such as The New Yorker still retain use the former type of diaeresis as a matter of style. Although the terms umlaut and diaeresis are often used interchangeably, they actually represent two different types of characters that happen to look alike.
When typesetting text, it's important to determine which type of usage the organization desires. For that reason, a little knowledge of the proper usage of umlauts and diaeresis can be important in desktop publishing.
For more on the history of the diaeresis (it developed from the use of double vertical lines in Latin verse) and its use in various languages, see diaeresis@everything2.com.
