I could be wrong here, very wrong.
My understanding has always been: -
Upon you arriving in a system you've never been to before it will be undiscovered to you, hence receiving the message "X No. of Objects Discovered" upon arrival and on result of you Honking.
If you then carry out a detailed scan on one of the discovered objects, excluding asteroid belts, you will accumulate exploration data. On handing this in you will be paid for it even if the object was already discovered by someone else. Should you have been the first person to have discovered the object, not only will you be paid for your detailed scan but in addition a 50% bonus for its discovery.
You've said that "
every system I've come to so far since I left the bubble has been "discovered" but not "explored" I'm assuming that means no cartographic data is available" this unexplored refers to you and you alone, that is that you haven't explored the system by detail scanning the objects, even though some one has been there before you. Go ahead and scan away, excluding the asteroid belts as you don't get paid for these, you will be paid but just won't get the 50% First Discovery Bonus.
I hope that helps clear things up a little for you?
To answer your thread title "Just checking - unexplored? By anyone, or just by me?" = Unexplored just by you.
This visual guide might be of help to you in giving you an idea of the worth of objects scanned.
http://imgur.com/a/VJ5wp
Also, if you want to keep an average running total as you explore along with a log of where you've been you might want to consider using Captains Log.
https://forums.frontier.co.uk/showthread.php/155545-Explorer-s-Application-Captain-s-Log