The problem phrasing the best possible answer to your question is around the word zap.
In my head a zap is a payment. Money moving from wallet to wallet. And i think for a lot of new Nostr users without lightning background they will associate a zap with a payment. But in reality (in the nostr world) a zap is a payment + some events around it (to tell the network about the payment).
So the answer to your question depends on the client implementation and the protocol but i'll try to summarise:
WebLN and NIP57 zaps should trigger ZapReceipt (which can be gamed) but it's telling the world you zapped. But the client can choose not to implement ZapReceipt events
With NWC and NIP-47 the wallet service is responsible for sending the payment receipt (kind 23195).
Nutzaps and NIP-61 it's the sender (client) that sends a kind 9321 to let the receiver know.
A little messy :-)