AT (Advanced Technology) and ATX (Advanced Technology Extended) are two incompatible power supply standards. While both power supplies share some of the same connectors, the technology behind both of them is quite different, requiring different motherboards and computer cases. The AT style was used from approximately 1980-1997, while the ATX standard is current.
Main Power Connector
The main power connector on AT and ATX power supplies are very different, and require different motherboards because of this. The main power connector on an AT power supply is actually two separate six-pin connectors that plug into the motherboard side by side in a single row. The ATX main power connector is a single 20 or 24-pin connector that places the pins on two rows.
The power switch of AT style power supplies is integrated directly into the power supply itself. This is a physical switch that turns the power supply on and off. ATX style power supplies use a "soft switch" that is controlled by the motherboard. This enables a computer with an ATX power supply to power off via software.
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Older power supplies provide a lower wattage rating than newer ones. Newer ATX style power supplies typically provide 300 or more watts, whereas AT style power supplies typically provide wattage of less than 250.
Though AT and ATX power supplies share many connectors, ATX power supplies may have connectors, such as SATA and 4-pin ATX12V, that never appeared on AT power supplies due to the technology post-dating the AT power supply. Additionally, an AT power supply has more mini-Molex connectors for devices such as floppy drives.