If you look carefully at the picture above you can see that four of the pins are square and the other four have rounded corners. The 8 pin 12 volt cable is polarized so it can only be plugged into the 8 pin motherboard connector correctly. It is often refered to as an 'EPS12V' cable. Depending on the power supply, the connector may contain one 12 volt rail in all 8 pins or two 12 volt rails taking up 4 pins apiece. But as time has passed many CPUs require more 12 volt power and the 8 pin 12 volt cable is often used instead of a 4 pin 12 volt cable. This cable was originally created for workstations to provide 12 volts to power multiple CPUs. If you plug the two pieces of a 20+4 power cable together then you have a 24 pin power cable which can be plugged into a 24 pin motherboard. The 4 pin piece is not compatible with any other connectors. Be sure to leave the 4 pin piece unplugged even if it fits into another connector. If you leave the two pieces separate then you can plug the 20 pin piece into a 20 pin motherboard and leave the 4 pin piece unplugged. A 20+4 power cable has two pieces: a 20 pin piece, and a 4 pin piece. Many power supplies come with a 20+4 cable which is compatible with both 20 and 24 pin motherboards. Motherboards can come with either a 20 pin main power connector or a 24 pin main power connector. It's better to first see if you can get a 24 pin cable to fit into a 20 pin motherboard before resorting to an adapter. Adapters also slightly increase the voltage drop which is something worth avoiding. But you should avoid using that kind of adapter if you can because the extra wire and connector are just more things which can go wrong. The 24 pin cable plugs into one end of the adapter and then the adapter plugs into the 20 pin motherboard. If you can't get them to fit together then you can get an adapter cable which will make it work.

You can solve that problem by carefully shaving down one end of the 20 pin motherboard connector. Or sometimes the end of the 20 pin motherboard connector is too thick to fit between the pins of the 24 pin cable. The only problem you can bump into (literally) is if there is something blocking the spot where the 24 pin cable hangs over the end. But it's okay to leave those 4 pins disconnected because a motherboard with a 20 pin connector doesn't need them. The extra 4 pins were added to the 24 pin version of the cable to provide one extra wire for ground, 3.3, 5, and 12 volts. The 24 pin cable only fits into a 20 pin socket at one end so you can't plug it in incorrectly. The extra 4 pins on the cable just hang over the end of the motherboard connector. You can see an example in the picture above. If you have an ATX power supply with a 24 pin main cable, it's okay to plug it into a motherboard with a 20 pin connector. Unofficial cable/connector maximum wattage delivery for main rails Most newer power supplies don't provide -5 volts in which case the white wire is missing. Newer motherboards virtually never require -5 volts but many older motherboards do. The -5 volt line on pin 20 was made optional in ATX12V 1.3 (introduced in 2003) because -5 had been rarely used for years. These are pretty common on the 3.3 volt line in pin 13 but are sometimes used for other voltages too. Some of the voltage lines on the connector may have smaller sense wires which allow the power supply to sense what voltage is actually seen by the motherboard. The 24 pin connector is polarized so it can only be plugged in pointing in the correct direction. The extra pins made the auxiliary power cable unnecessary so most ATX12V 2.x power supplies don't have them. The new 24 pin connector added one line apiece for ground, 3.3, 5, and 12 volts. The older 20 pin main power cable only has one 12 volt line. The 24 pin main power connector was added in ATX12V 2.0 to provide extra power needed by PCI Express slots.

Standard 4.2mm Pitch ATX Header Connector Datasheet

Molex peripheral power connector