The LR44 battery and AG13 battery are exactly the same dimensions and are 100% interchangeable. They are known as many other names and are compatible with their silver oxide counterparts. The silver oxide version of this battery is usually preceded by the letters SR.
As one of the most popular button batteries it has more than 20 different names. Examples are L1154, L1154C, L1154F, L1154G, L1154H, LR44G, LR44GD, LR44H, LR1154, LR44, LR44H, PX76, PX76A, R357/7, RS76 and the list goes on.
In conclusion the LR44 battery is compatible and interchangeable with the AG13 battery. There is no difference at all besides the naming convention.