Mechanism of Stop Loss

When a trader punch in a stop-loss on its broker terminal, where is it stored till execution?

At the exchange, or at the broker?

If at the broker, can the speed of broker-execution/execution-latency be different among different brokers?

If yes, where Zerodha stands in terms of Order Execution Latency?

Reason for asking - Noticed better Stop Loss Price Execution at other brokers consistently, compared to Zerodha. So, wanted to understand the reason behind it.

At the exchange, so nothing to do with broker.