EDIT: No matter how many times I edit this, this reply never seems to get any shorter.

I hope this helps to explain the situation a little.
I feel that forum topic does give enough information to definitvely say that the Administrator group is different in functionality from the Built-in Administrator account.
But you're right it doesn't explicitly say that Administrator users act differently. Lots of implications and implied statements but nothing explicit. And I full acknowledge I'm finding many posts online that suggest the difference but no definitive documentation from Microsoft listing those facts. I don't know if I'm just searching incorrect terms or what. But I'll keep searching.
I did, however, find something that you might find interesting.
UAC: Admin Approval Mode
http://windows.microsoft.com/en-US/wind ... roval-Mode
Built-in Administrator Account UAC Admin Approval Mode
http://windows.microsoft.com/en-US/wind ... or-account
Both of those articles are about Admin Approval Mode. For the UAC Admin Approval Mode is Enabled by Default. For the Built-in Administrator Admin Approval Mode is Disabled by default. That if you disable AAM the UAC is also turned off.
In my link to the Forum Topic they mention specifically that the Built-in Administrator turns off the UAC by default. Which matches the articles above. If the UAC needs the AAM, and AAM is disabled by default for the Built-in Administrator then so is the UAC.
If the AAM is turned off you will never be prompted for permission to run a program with Administrator Privileges. If it's turned on you will be prompted every time you try and run a program with Admin privileges.
So, right-click on a program and select "Run As Administrator" and see if it prompts you. If it does, then AAM is turned on. If AAM is turned on, and the Administrators Group auto ran every program with Admin privileges it would prompt you every single time you ran a program. If, however, the AAM is turned on but Administrator Group users ran only with the least required privileges then the prompt would only happen with those programs that specifically requested elevated privileges or those that the UAC recognizes as needing such privileges.
This is the difference. The Built-in Administrator, needs to be manually turned on and by default turns the UAC off preventing these prompts. The Administrators Group does not turn off the UAC and therefore the prompts continue but only when the program needs to run with Admin privileges. Which few do.