I hold no security clearance...but my impression from a few places is that "Classified", in the context on NATO, generally means "half a notch more secret than whether the NATO HQ cafeteria is serving donuts with breakfast today". Why: with ~30 member nations in NATO, most of 'em with counter-espionage and cybersecurity budgets which wouldn't even be a rounding error for the U.S., it's reasonable to assume that the Russians (& other countries with "A List" intelligence capabilities) are getting timely copies of any mere "Classified" stuff.
(I may be confusing "Classified" and "Confidential" here...but I've no reason to believe that either Bleeping Computer or their sources really know NATO's usage, either.)