The main difference between a zinc battery and an alkaline battery is the type of electrolyte used in both batteries. Because of the composition, an alkaline battery delivers more energy than a zinc battery. Both batteries should thus be used in different appliances.
Zinc air battery are different from other batteries. They do not contain active materials in their positive electrode. This type of battery reacts with air - so it’s important to remove the tag before inserting the battery into your device. They provide a current of 1.4V if used correctly.
Whereas some size change is perfectly normal, it should not be overly pronounced. If so, replace the battery immediately. A bulging coin battery may lead to device malfunction and even short-circuiting.