If you ever had a car with both you would find out that a cigar lighter will not work in a power socket. They are not the same.
My PT also had 3. The cigar lighter only worked in the lower front one and that one only had power when the key is on.

My cell phone charger doesn't stay in the cigar lighter socket very well.
It works great in cars with power sockets.

That is just the way they make them. Power sockets have the capacity for a bigger current draw.