AT- hardware power control. ATX- software power control, different power connectors, different keyboard connection, different size. AT is the older size/format, mainly use up till the late 90s. ATX...
For the most part it's size, and AT is very old computer wise. See here for more detail: http://www.devhardware.com/forums/motherboards-32/at-vs-atx-179846.html
There are many differences between AT and ATX motherboards.
The most noticable, without disassembly, are probably the keyboard connector (AT is much larger) and the power switch. The power switch...