Choose Zotero Standalone if:
Zotero Standalone (unlike Zotero for Firefox) runs as a separate program instead of part of your web browser.
It works with Firefox, Chrome and Safari.
Download [link here] and install Zotero Standalone just as you would any other program. You will also need to install the Connectors to allow your browser to save items to your Zotero library.
You can install both Zotero Standalone and Zotero for Firefox and use both on the same computer.
Choose Zotero for Firefox if:
Zotero for Firefox runs as a plugin for the Firefox web browser, not as a separate program.
The same version of Zotero for Firefox works on any computer that runs Firefox; there are no separate Windows and Mac versions.