Cryptocurrency vocabulary is difficult to pin down. Although both involve receiving* tokens without consent, I view an airdrop as a dismemberment that occurs on a preexisting chain and a hard fork as an appropriation of tokens** on a separate chain. There are many ways an airdrop can be executed. Tokens are pushed to end-users using some heuristic. Maybe they are sent to all users with more than 0.1 ether or with a nonce more than 10. Users opt-in to the airdrop and receive tokens of their own volition.
Since Ethereum 2.0 is an upgrade to Ethereum 1.0, users won't receive an airdrop or a ratio of tokens based on their eth1 balance. Ether in eth2 is completely fungible with eth1 ether. There are some technical challenges that will most likely not allow ether to flow freely from eth2 to eth1 in the beginning. There is a plan to transition eth1 into a shard on eth2, at which point the eth1 and eth2 ether balances will be reconciled together under the same protocol.