Connected Standby is a system-wide power state. During Connected Standby, many devices are powered down, including network adapter(s). In fact, from the perspective of the NDIS miniport driver, Connected Standby looks similar to a system sleep (S3) in Windows 7: NDIS sets a few wake patterns, then sends an OID_PNP_SET_POWER (e.g., D2 device state). That's it.
Where Connected Standby is wildly different from prior OS releases is in usermode sockets. In Windows 7, the OS would never put a network adapter into a D2 power state unless nobody is using it. (Mainly if the system itself goes to sleep, or if an Ethernet NIC is disconnected). But when in Connected Standby, the system will put the NIC into a low power state even if the NIC is being used. The system will pretend that the NIC is still connected, and the system periodically wakes up to renew its IP address. Critically, the system also plumbs a special wake pattern onto the network adapter. If there is an incoming notification for that system (e.g., an incoming chat message), then the Microsoft notification service (a remote server) will send a matching packet to the system, waking it. You might think of it as cloud-scale wake-on-lan.
To answer your questions:
Connected Standby will only be enabled on systems that are designed for it. For traditional desktops / laptops, it's business as usual (sleep, hibernate, etc.). The OEM has to put a special marker into the firmware to indicate that the system is designed for Connected Standby. Because of this, any existing system today will not enter Connected Standby; only new systems released with and designed for the next version of Windows will use this feature.
Always-On/Always-Connected (AOAC) is the name of this feature. Connected Standby is the system state that an AOAC-compliant system can enter.
See #1.
Not all drivers are required to implement AOAC. However, if you want to sell your chip to an OEM that is manufacturing AOAC systems, then obviously you will need to meet the requirements for Connected Standby. Also, if you intend to get a logo, note that there are big logo requirement changes for WLAN/WWAN even besides Connected Standby, e.g., Selective Suspend.
I'm not familiar with Intel AOAC. I speculate that if Intel had been using "AOAC" prior to Microsoft's public discussion of AOAC at //BUILD, then it could just be an acronym coincidence.