I thought a airdrop didn't necesarely should have to be a fork.
because I see a lot of websites advertising with a airdrop for a ico
Airdrop is a part of a marketing strategy of some certain ICO, and most of ICOs use token created on the Ethereum blockchain, so it is not a fork usually, but a token.
Of course, some airdrops are held because Hard Forks take place, but it is a special case.