Yes, what wsieber said. The diaeresis is a diacritical mark, and umlaut is etymologically a phonological process (though it is now used in English to refer to the diacritical marks). In German, the sounds transformations are as following: /a/ -> /e/, /o/ -> /ø/, /u/ -> /y/. In addition, the origin of the diaeresis is from a small e placed over the vowel undergoing umlaut. This same process happenes in most Germanic languages: e.g., foot ~ feet, mouse ~ mice, etc. These words were originally two syllable in the plural, and the vocalic sound in the final syllable, which is now gone, modified the vowel in the first syllable.

Umlaut 'umlaut' is from German um- 'about, at' + laut 'sound'. There's a similar phonological process called ablaut 'vowel gradation'. This is the process that shows up as sing ~ sang ~ sung in English and which goes back to PIE.

Ceci n'est pas un seing.