ELECTRONIC, MAGNETIC, OR RFID?
'Electronic' pet doors sense a collar key, then unlock or actually open. A number of different kinds of collar keys have been used to trigger magnetic pet doors including infra-red, high-pitched sound (ultrasonic), magnets, and most recently, radio-frequency identification (RFID) chips.
In the case of the magnet type, the pet door senses the magnetic field to activate. In all cases, the pet door must be powered with either batteries or an ac adaptor. The collar key itself may or may not be powered. A magnet, for example, requires no power. The RFID type are also passive and require no batteries.
An infra-red or ultrasonic transmitter does require small, hearing aid type batteries.
Less expensive electronic dog doors simply unlock and require your pet to push through. More exotic versions are actually motorized and open the door for your pet, then close behind him or her.
By contrast, "magnetic" pet doors use only magnets for collar keys and rely upon the strength of the magnet to actually unlock the flap. Since the magnet does the work, the pet door requires no power to operate making them very handy for installations in areas where power isn't available. They are also not affected by a power outage or dead batteries. However, the magnets in these type of doors tend to be stronger and may be more likely to pickup metallic debris or to startle the cat by suddenly attaching to something.
So what is an 'automatic' pet door? It could be any of these!