As the name implies, extensions serve to "extend" the capabilities of BeEF. Extensions differ slightly from modules. They are a way to add new functionality to the core features of BeEF whereas modules usually have a narrow set of abilities that perform a specific task. This helps prevent feature creep by modularizing new core features. So if you're asking yourself...
Does it change the way BeEF behaves? Extension
Does it change the way zombies behave? Module