Which one is the mini pci, mini pci-e, mini pci-e half?
Neither device is a Mini PCI Card. PCI and PCI-E are completely different standards. The Intel Card based on its size is a PCI Express Mini Card.
Dimensions of PCI Express Mini Cards are 30 × 50.95 mm (width × length) for a Full Mini Card. There is a 52-pin edge connector, consisting of two staggered rows on a 0.8 mm pitch.
The Atheros Card based on its size is a Half PCI Express Mini Card.
A "Half Mini Card" (sometimes abbreviated as HMC) is also specified, having approximately half the physical length of 26.8 mm.
Both devices are Mini PCI Express which means they both will work unless the OEM has blacklisted one of the devices and/or they are both not on the whitelist of allowed devices which can happen with these particular type of devices.
Did anybody has tried so far whether is it working?
Source: Wikipedia - PCI Express