It depends on the flow rate of your shower. It’s almost certainly much higher than your bathroom faucet. Faucets usually have aerators, which constrict flow to avoid splashing and to save water. Yours is probably around 1GPM (Gallons Per Minute). Most showers are around 3GPM.
So when more water flows through, the faster the hot water from the tank reaches you.
Flow rate. A shower puts out around 6-10 liters per minute, while a typical sink faucet is around 1-4 l/m
This also depends on the length of piping between the water heater and the given outlet. It’s likely that the way your own shower is plumbed, the pipes are shorter between the shower v.s. the bathroom sink.
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