POE = Power-Over-Ethernet which IMHO is superior to regular wired cameras. You just run an ethernet wire to each camera.
NVR = Network Video Recorder. With POE cameras you have to have a POE network switch, which in most systems is built into a DVR (digital video recorder)
Anran = Some crappy chinese camera company
Amcrest = Some other camera company
NVRs do have the ability to record on motion trigger or record all of the time, most of them can also text you recorded clips, etc. My 8 camera 2TB system records 1 week of video on all cameras.