The distinction being that anytime access is "I'm not flying today, Qantas, but I'll hang out in your (domestic) lounge" – something which some people here will see as a great and cool thing, but others will see less appeal and arguably many CL members are simply too busy to bother with coming to the airport for a free feed and drink unless they have a meeting there – whereas any airline access is "I'm not only not flying with you, Qantas, I'm flying with a competitor and sending them probably thousands or even $10,000+ of my money, but I'll hang out in your first class lounge and you can pick up the tab, thanks very much, now where's that basket-pressed Shiraz?".
To me, that's quite some distinction.