Thank you for the clear explanation. I was aware what ATX and Micro ATX were but not aware of the ITX.
Is ITX the standard Intel was pushing 4 or 5 years ago?
No, that was BTX. When the Pentium 4 was overheating and Intel was having a lot of issue competing against the first K8 Amd chips, Intel wanted to set a standard for motherboards that set airflow and cooling as the top priority, over cost of components and production. None of the pcb manufacturers wanted anything to do with that, as they saw it as Intel's problem, and then the first Core processors and soon after Core 2 duo processors came out, which did not have the abnormal heat issues of the Pentium 4s, and the whole idea was scratched.
Shortly after, AMD proposed the DTX format, which would have been a board just slightly smaller than the micro ATX format, but would have been the cheapest for pcb manufacturers to produce, but would require all case manufacturers to add a few standoffs onto their mounting hardware that they didn't previously. Despite it being a win-win type of proposition, they really wasn't any interest in it, either.
ITX was coming up during all of this, and focused solely on getting full-sized PC components into smaller than micro ATX systems. Because Home Theatre PCs were coming of age at the same time, the two started to go hand-in-hand, and both are now the basically directly related and the third size standard. An ITX motherboard is basically a square with the dimensions being a square of the rear panel which has been standard sinxe ATX came around.