AirDrop while connected to a WiFi

I believe AirDrop will first use Bluetooth to make the connection, and then, switch to Wi-Fi. If no Wi-Fi network is available, AirDrop will use a peer-to-peer (Ad Hoc) Wi-Fi network to connect both devices. So, in the scenario you described, it would connect to the same Wi-Fi network as the other devices use.

This article is fairly short but may help you understand.

https://www.lifewire.com/what-is-airdrop-how-does-it-work-1994512

I think while the airdrop is happening the computer would be exclusively on the peer to peer network as wireless is limited to a single Tx or Rx response at a time.

Can a single WiFi card establish multiple WiFi connections or do they use an extra/special WiFi card in their devices?

Your question is a good one.. and the answer is NO.. a wifi card can only have one connection.. that is why for airdrop to work it must be connected to the same router and usually same band. People do have lots of issues with airdrop if they use multiple AP and especially when they are independent of one another.

You could test this by downloading some big file.. linux iso is the typical download.. and using airdrop at the same time.. while keeping track of the download via activity monitor. Fact is wifi is limited.. and cannot do multiple connections, although it might have some time slicing ability.

Bluetooth btw is built into the same wifi card but uses separate chip.. and will work simultaneously with the wifi.