It's somewhat analog to OSX. The kernel and low-level services are open-source and made publicly available on http://opensource.apple.com/. From that point and up, OSX is proprietary. Android would be somewhat analog to Darwin + Finder being open and iTunes, iPhoto, Mail and others being proprietary.
yeah, somewhat. that being said, AOSP does provide a little more than Darwin does, mainly, there is some UI provided. Otherwise, .. yeah. It's also getting closer and closer to that model.
It provides a lot more, otherwise Cyanogenmod wouldn't be possible. I have a cheap Huawei phone and replaced the annoying stock firmware with KitKat per Cyanogenmod and it's virtually impossible to see the differences compared to my Nexus 4 besides logo's and the extra features that Cyanogenmod has (I installed the Google Apps bundle).
At this point in time, it would be nearly impossible to make an open source, fully compatible, version of OS X. Replicating the APIs and user interface would probably cost hundreds of millions and a few patent lawsuits.
as you said, you installed the google apps. well, google apps are 100 megs. guess why. Its not just gmail and what not. It includes all the proprietary APIs, everything.
You don't get any of that in AOSP. Reinstall CM but do not installed gapps, and you'll have something close to AOSP (well, better than AOSP still)
I bet you don't last a day before you'll install gapps again (and thus all the google proprietary libs, etc.)