They use different cells:
-The powerbank uses 18650 cells all in parallel, most likely 6x 3,350mAh = 20,000mAh
-The jumpstarter uses high discharge LiPo, 3x in series for 11.1V nominal, 12.6V fully charged
18650 cells are safer, but they have very limited output current, generally less than 3C.
LiPo cells on the other hand, have lower internal resistance, and can put out much higher current, some can reach up to 100C.
They work differently:
-The regular powerbank has a boost circuit to convert the 3.7V into 5V output.
-The jumpstarter has a buck circuit to convert the ~12V into 5V, and additionally an direct output from the LiPo batteries, this is what allows it to “start” the car. Your 13,600mAh jumpstarter should have 3x 4,500mAh LiPo cells in series, and if rated at 40C they should provide 180A continuos, and probably 3 times that much in burst.
The reason why jumpstarters are more expensive is because they come with a protection circuit that triggers in case of reversed connection to the car battery or short, otherwise it would explode. They also require integrating a balancing charger because the cells are in series.
Keep in mind that these jumpstarters doesn’t actually start the car, they just aid your existing car battery to crank the starter motor, they won’t work on a fully dead car battery. Regular flooded car batteries are rather old tech and they usually won’t provide enough crank amps at <60% capacity, this is why better options exists nowadays such as SLA deep cycle AGM or GEL.
I have a RavPower 14,000mAh jumpstarter rated 600A, and fully charged it was able to quickly start my 2.4L 4I engine 3 times. After the 3rd attemp I needed to leave it connected much longer, the powerbank still had plenty of capacity, but it was the car battery which was discharged.
I hope this answers your question. 