You may need to use different bibliographic styles for different classes. Zotero lets you switch between styles easily. Your citation information is saved in a neutral format and can be converted on-the-fly to whatever style you need. From a single Zotero library, you can generate bibliographies in any of Zotero's thousands of styles.
In the "preferences" pane of Zotero, you can choose a default style, which you can change at any time.
If you need a stlye that isn't listed in this window, click "Get additional styles..." to visit Zotero's massive style repository, where you can download any style you need.