4 Pin Aux connectors are used by some video cards to provide additional power to them via the power supply.
provide more power for the CPU
The purpose of a 4-pin auxiliary connector on a motherboard is to provide an additional 12V power supply to the processor.
To provide power to a circuit board or fan
24 pin connector is required to supply power to the motherboard.
Yes, it can be normal for a computer to only power on when the 20+4 pin connector is plugged in without the additional 4-pin connector, but this usually indicates a problem. The 4-pin connector provides extra power to the CPU, and without it, the system may not function properly or could be unstable. If your computer operates only with the 20+4 pin connected, it's advisable to check the 4-pin connector, the motherboard, or the power supply for any issues.
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AUX
If it as a 20 or 24 pin connector and a 4 pin connector then it is a ATX power supply.
4-Pin Berg connector
A regular ATX motherboard uses a single 20-pin P1 connector with optional 4-pin auxillary power connector
4 pin and 6 pin. 6 pin provides power for the external device.
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