WiFi Direct is very much NOT Ad-hoc mode.
Ad-hoc mode is a very old means mode for direct device to device linking without an access point (AP). This was introduced for basic connections in 802.11b, and essentially frozen at 802.11b specifications. Which means that Ad-hoc is limited to 10Mb/s connections and either open or WEP encryption.
WiFi Direct is something new. The small picture goal is the same as Ad-hoc, forming a direct connection between two devices. But in the big picture, the reason for the connection computer to device connections, the same basic idea as Bluetooth. So I might use WiFi Direct to send an image to a printer or digital picture frame, transfer a video from one phone to another, tether my laptop to my phone, etc.
Wi-Fi Direct uses Ad-hoc for basic discovery -- the two devices rendezvous and share capabilities. At this point, one of them will go into AP mode (Wi-Fi Direct devices have to support AP mode), and they run a Protected Setup, which allows the connection to be secure and full speed, without any need to manually enter passcodes.