I'm no expert on military terminology, but I think you can replace "air strikes" with "air raids" or "air attacks". All three phrases mean the same thing to me, but I don't believe "air raid" is as common now as it once was.
I would say that air strike comes from AE.
In the UK, during World War II, we had air raid shelters to give protection against air raids. Air strikes also sounds as if they are targeted, while air raids are more widely spread, being aimed at towns rather than specific buildings or people.