ATX power supplies have been the standard for computer desktops since 1995. There is a newcomer, called EPS, that's challenging the rule of ATX power supplies.
ATX power supplies have a 20-pin main power connector, whereas EPS power supplies have a 24-pin connector.
ATX power supplies contain an additional 4-pin +12v connector called a P4 connector. EPS power supplies have an 8-pin +12v EPS connector that's essentially two P4 connectors combined.
EPS power supplies contain a 6-pin PCI Express power connector to provide additional power to PCI-e video cards. ATX power supplies don't possess this connector.
There are three connectors that both the ATX and EPS power supplies have in common: peripheral power connectors (commonly called Molex connectors), floppy power connectors and SATA power connectors. However, some older ATX power supplies may not have the SATA connectors.
A large number of EPS power supplies have the ability to "split off" the extra pins on their power connectors, making them backward-compatible with ATX motherboards. Although there are adaptor kits available that claim to enable an ATX power supply to work with an EPS motherboard, manufacturers don't recommend this, because it can reduce functionality and performance.
Although it's possible to use some EPS power supplies on ATX motherboards, ATX power supplies don't have the connectors necessary to adequately provide power to an EPS motherboard and its components. Consult your motherboard manual, and use the power supply it recommends for best results on your computer system.