Ainur were the "angelic" beings who existed with Iluvatar before the making of the world. The Valar were those of the Ainur who, being enamoured with the vision of Arda, descended into the World to be its guardians. Thus, many of the Ainur (perhaps hundreds, or thousands) remained with Iluvatar and "come not into this tale" as Tolkien liked to put it. The lesser of the Ainur who accompanied the great ones into the World are called Maiar. Whereas we don't know the number of the Maiar, all the Valar, along with Melkor, are named in the Silmarillion.
That said, in early versions of Tolkien's legendarium, there were a lot more of the Valar, which have subsequently been abandoned. For example, the "war gods" Makar and Meássë. http://www.silmarillionwritersguild.org/reference/characterofthemonth/makar-measse.php