What differences are there now adays from Chrome OS and the Android OS? At some point, Chrome OS had no relationship with the Android OS.  

Then several years later, there was some minimal integration.  

After that years later once more the Chrome OS is capable of accessing the full Android Play Store and installing Android apps.

But the Chrome OS is not the Android OS.  I can't seem to get an understanding of what the relationship is with several articles that I was trying to read up on.  Does the Chrome OS just have the Android OS installed along-side it and it calls into the Android OS for handling all Android app interactions?

That is my assumption.  It likely doesn't even use the majority of the features on the Android OS (or shouldn't need to) in order to get tasks done. Does anyone have any input that could provide me with some clarity?
Android on Chrome OS (ARC++) is just one supported container flavor sitting on top of the Chromium/Chrome OS kernel. Not all features of Android are supported, the version of Android (Nougat) that Chrome OS is running depends upon the version of Chrome OS.
See: Running Custom Containers Under Chrome OS for more details regarding containers on Chrome OS.
So while Chrome OS has a high security reputation, getting Android to run on a Chromebook means some compromises:

Don't Android apps (ARC++) run in a container and not a VM?
Unfortunately, yes, Android apps currently run only in a container. We try to isolate them quite a bit (using namespaces, seccomp, alt syscall, SELinux, etc...), but at the end of the day, they have direct access to many syscalls and kernel interfaces, so a bug in there is reachable via code compiled with Android's NDK.

Additionally while Google is trying to promote Android on Chrome OS to developers: https://developer.android.com/chrome-os/ there are still outstanding issues like getting Android on Chrome OS to see the SD card in your Chromebook which might be considered showstoppers by certain apps.