Well, certainly most major airports are not in the city limits. CPH, OSL, ARN.... all of them are a good distance from the city. Same for ZRH, VIE, MUC, FRA, LHR, CDG, FCO... There are only very few true inner-city airports... like LIN or LCY. Not even something like BOS would qualify for that.
For me, it means "Can I get from the airport terminal to the city center within 30+/- minutes". Ideally with a train/subway/metro. And then CPH, OSL, ARN, VIE, ZRH are named accordingly. Since, from CPH, I take the metro and I am downtown Copenhagen after 15-20 minutes. The Arlanda Express or the OSL Train (not talking about the ridiculous pricing of those) take me to downtown Stockholm or Oslo.
But when I book Copenhagen and got dropped off in the middle of nowhere in Skane, or book Vienna and end up in Bratislava... that is just messed up. (which btw IU also hate about Newark, which a lot of people sell as New York. And especially for Germans hard to phonetically understand that there is a difference between "newark" and "newyawk". Many many years ago, the first time I landed in EWR, I was kind of lost... what I am not in New York?
But well... you can also book Bordeaux and end up on Porto