The ‘deck overview screen’ is not the screen with the deck tree, and the manual page you linked is agreeing with the actual GUI there. But as for the deck tree screen, I agree that the third card column should be labeled ‘Review’.
The search syntax is also correctly documented, and I don’t see a problem with how it uses the word ‘due’. In short why your numbers don’t add up: prop:due=0 is not the same as is:due, and is:review and is:learn are not mutually exclusive. See the link for more information.
They’re not different things. The first one is only more powerful syntax, which in this case allows you to ask for “cards that have become due today”, whereas the second one can only mean “cards that have become due”. The latter can also be written as prop:due<=0.
Due was originally chosen over Review for the deck list screen to try to keep the width of that column down. Learning cards are also due, and we now show them separately, so it’s potentially more confusing than it was in the past, and perhaps we should change it.
In both prop:due=0 and is:due, “due” is carrying the same meaning, which to my understanding is the point of this thread. But obviously, the two searches are not the same, because they contain other stuff as well.
E.g., strawberries and raspberries are aptly named, because they are both berries. But that doesn’t mean they are the same.