For example, I want to draw a teal circle with part of an orange circle on it.

When I select them both and choose "make clipping mask", it gives me the correct orange part, but the teal part is now invisible:

[![enter image description here][1]][1]


Here is what happens in Photoshop and what I'm trying to achieve in Illustrator:

[![enter image description here][2]][2]


  [1]: https://i.sstatic.net/g3jfc.png
  [2]: https://i.sstatic.net/wJoiL.png