Also, strictly speaking many Jews are "Messianic" in that they believe in the coming of Moshiach (Messiah). But when I speak of "Messianic Jews", I am speaking of those who recognize Y'shua (Jesus) as Messiah. They are not waiting for the coming of Messiah, but rather the return of Messiah.
The Congregation I attend, Beth Simcha (House of Worship or Joy), is aligned with the MJAA as our overseeing body. (Actually it is the IAMCS - International Alliance of Messianic Congregations and Synagogues. Which is an arm of the MJAA. Dont'cha just love all the alphabet soup stuff?)