Does task manager run as administrator by default on Windows 10?

I was trying to close a non-responsive process, and after the first time I clicked "End Process", nothing happened. So I did it again and this time a window popped up saying "Access is Denied". Eventually the process did close, but this got me thinking..

If I had ran task manager as an administrator, would it have still gave me this "Access is Denied" message? Or, in-fact, does Windows 10 run task manager as an administrator by default (when the user account is an administrator). Furthermore, is there any difference between running it as administrator or not?

Running it as admin via this method:

I don't see any noticeable differences between that and just doing Ctrl+Shift+Escape.

Note: This question is specifically for Windows 10 (and possibly 8/8.1) and I am running Pro. Also, my UAC set to 'Never notify'.

Answer

Does task manager run as administrator by default on Windows 10?

Only if it is being run from an administrator account. Ben N's answer below has a great explanation of how this is actually implemented.

If I had ran task manager as an administrator, would it have still gave me this "Access is Denied" message?

Yes. There are plenty of processes that even an administrator is not permitted to end. Furthermore, trying to end a non-existent task also produces this error message.

If the reason you had got the "Access is Denied" message was due to Task Manager not running as Administrator, you would get this very explicit message telling you so:

Furthermore, is there any difference between running it as administrator or not?

Yes, but you'd have to run it from a non-administrator account to see it.

Incidentally all the above behaviours are exactly the same as in Windows 8/8.1