There are plenty of polynomials, and only a few are specializations of Macdonald polynomials. As a polynomial botanist, the following is a very incomplete family tree.

[A more comprehensive list of symmetric functions and generalizations can be found here.][1]

[![polynomials][2]][2]

Edit: I added a few more generalizations, but it is getting crowded. Click on the image for a larger version.

[![bigger graph][3]][3]


  [1]: https://www.math.upenn.edu/~peal/polynomials/polynomialindex.htm
  [2]: https://i.sstatic.net/g5925.png
  [3]: https://i.sstatic.net/PS9jA.png