Zotero is a freely available extension for the Firefox web-browser (or can be downloaded for the Chrome or Safari connector) that runs in its own pane, separately from web pages. It automatically detects content in your web browser, allowing you to add to your personal library with a single click.
Zotero Standalone is an application that you can download from zotero.org. It plugs into your browser of choice, and comes with connectors for three browsers: Firefox, Chrome, and Safari.
You must have Zotero Standalone open to use the Firefox, Chrome, and Safari capture icons. (If you don't, you will just be redirected to Zotero's website.)
You do not have to install the word processor plugins with Zotero Standalone. The plugins are bundled with the software download.