As was pointed out in the entry on the word airline, “airline” and “air line” are not synonyms. I talked about airline in the previous entry, so I won’t say anything more about it here.
According to The New Penguin English Dictionary (1986), air line is chiefly a North American term. It is synonymous with beeline.
That was news to me. It was not the beeline part that I was unaware of, although that too. It was the North American part that I surprised me. The reason is, despite being a Canadian and Canada being part of North America, I’d never before heard the term air line used this way.
Now I know, but, for a couple of reasons, I’ll probably still use the term beeline rather than air line. First, in my opinion, beeline sounds better and, unlike air line, can’t be confused with airline.
Second, a beeline is a straight line between two points. I’ve never studied bees, but I would imagine that they generally try to follow reasonably straight lines from hive to flower to flower to hive. Air traffic control rules and air traffic controllers, on the other hand, often force planes to fly routes that are not straight lines between the departure and arrival points.
Thus, at least as far as I see it, which might just be a result of being ignorant of bee behavior, beeline depicts the concept better than air line.