the person who requests a zap invoice embeds a signed note into the invoice, called the zap request (kind 9734). this is how you know a person initiated a zap toward you. you don't know for sure if they were the ones who paid it, but its implied.

the lightning node that sends the zap is another signed note (the zap kind 9735). they are typically two different keys. you list the lightning node pubkey in your lightning address and clients use that to authorize zaps from that node.

A user does not send the zap, only the lightning node does when it receives confirmation of payment.