It depends on the NAS, some makes like Synology and QNAP have a camera solution built in. Otherwise, you're better off with an internal drive for most NVRs just for the read/write speed alone.
That really depends more on the cameras/NVR than the alarm. The typical arrangement is that the alarm has an output that is wired to the cameras/NVR, and upon trigger the camera/NVR sends a snapshot to a pre-arranged address. Some cameras and NVRs have this ability built in, some can have it added, some cannot.
Here is the device I use when needed for my installs.
https://www.axis.com/products/axis-t6101