Printing something on a piece of paper is not counterfeiting under any forelorn definition. I printed business cards on obsolete Yugoslavians notes, notes that have no value in Canada, and no status in Canada. They are not legal tender anywhere. They were sort of cute, made an interesting business card if nothing else. They were not sold, but made up for a particular client who wanted something different.
We had a discussion some time ago about and 1898 $1 note with an extra 0 added to make it look like a $10 note. Although no similar note was produced (which a good collector can look up in his Charlton), I feel such items are counterfeit, a great many other people on here did not agree.
Adding something to a note which makes it appear to be something it is not, is counterfeiting. Adding a flag on the back or a postage stamp, or one of those notes that are counterprinted to trace the travels of the note is not counterfeiting, just a little picture added. Amazing what some people wll do to diddle a note. Of course, no real collector wants such items.
Rick