I have a 10,000mAh regular power bank but the size is much smaller than this 6,000mAh Cellink battery. Why is it so?

mAh rating can be misleading if we don’t consider voltage. Tip: think in terms of Watt-hours (Wh). Of course the type of battery should be taken into consideration: high power density batteries have higher capacity for a given volume. In other words, at same capacity, a Li-ion or LiPo battery will always be smaller than a LiFePO4 battery. Still, you should keep in mind that consumer electronics and car accessories assume different voltage values. The milliamp rating of regular power banks is usually based on a voltage of 3.7V. This means for a 10,000 mAh battery, the total capacity is 10,000mAh x 3.7V / 1,000 = 37Wh. By way of comparison, the Power Magic Ultra Battery has a capacity of 6,000mAh at 12.8V, which translates into 76.8Wh.