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 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.