The Huawei 4G stick E3372-325 does not work with the FritzBox 7530, as this stick does not support all required AT commands and therefore cannot be controlled by the FritzBox.
Although a similar stick, the Huawei E3372h-320, works for you, the E3372-325 is explicitly listed by AVM as incompatible, which means that the FritzBox cannot establish an Internet connection via this stick.
There is no known alternative firmware that would make the E3372-325 compatible with the FritzBox 7530. A different LTE stick that is officially supported is therefore recommended for use with a FritzBox.
The 325 is a nightmare to run on Linux (look at the Digitec Reviews or search the Web).
Better get your hands on a E3372-320 (its predecessor), it just works.
Sorry. I don't know the exact difference either! But the E3372-325 is clearly made for travelling. Unfortunately, there's not much in the text for the one with H. The E3372-325 has a micro SIM and the E3372h-325 has a mini SIM.