"Madam"/"Madame" Chair/man/person (was: Umlauts)

To take this a bit further off-topic (sorry) - what's with the
<Madam>/<Madame> spelling difference?

I was taught that a "madam" (or several "madams") ran a whorehouse,
while "Madame" (or several "Mesdames") was the title form.  But it
seems that "Madam" is used all the time in titles, including that
of Madeleine Albright's book, _Madam_Secretary_.

So what's the straight dope? :)

-Mark

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