It's like White Wolf's Vampire - The Masquerade:
All Nosferatu are Vampire, but not all Vampire are Nosferatu.
Or even more simply:
All Werewolves are Otherkin, but not all Otherkin are Werewolves.
I find the whole Angel - Archangel - Fallen Angel thing both needlessly complicated and endlessly confusing.
I looked for ages when I first realised I had wings, thinking I was a member of The Fallen. Read everything I could find, and quickly realised that I would need to live more than one lifetime just to unravel the basics of stories that have been told and re-told so many times that they are different in each and every land you gather them from. And the few Angel names that are known are not always included in the same groups by every story teller. Very baffling to the amateur scholar.
The main problem here is that when searching for yourself you look for truth. But in any part of this voyage of self discovery the best you can hope for is something which, like a bell, when you ring it, sounds true to you.
With the biblical angel thing that is not good enough. You have to accept all their truth or none of it makes sense.
I found that that was not for me.
Luckily a very good friend told me to count my feet, and when I looked down I had FOUR. That kind of knocked being a member of the heavenly choir on the head for me.

A little more research revealed the possibility of a tail (which I still haven't found!! But I'm patient.) and a love of good hay that could not be denied!

So one Pegasus later I still don't understand all the ins and outs of the Angelic choral system, but I do know there are said to be lots of different groups and levels of Angels/Fallen, and The Grigori is said to be one of those groups.