The only people I know who call tunes 'airs' even in liturgy are the Irish sisters who are students at the place where I work. In the parish choir, though, we tend to refer to a tune by the first line of the hymn text which usually goes with it' as in: 'What tune are we singing for 'O comfort my people and calm all their fear?' to which the answer is 'O purest of creatures'. (The tune in Celebration for Everyone has a nice English name but according to my Irish sisters has something to do with County Clare and has been known to reduce them to giggles when required to sing it in the liturgy.)
I've noticed people using hymn tune names especially when working with other Christians, particularly Methodists, who seem to have them all at their fingertips, while I'm going, 'Could you hum that for me and we'll see if I know it?' Something I seem to have missued out on during my Methodist upbringing...
-otherwise known as Londonderry Air, which I always thought was an affliction you got from travelling on the Tube too much. We say "what tune is that?" round here too, by the way. The term 'air' is rarely, er, aired.