Zotero is available as a Firefox extension and as a desktop program. If Firefox is your preferred browser, then you may enjoy the simplicity of using Zotero as an extension. However, if you use Chrome or Safari, then you can download the desktop version along with the connector for either browser (more on this later).
The two versions of Zotero are essentially the same, but there are some slight differences. For a detailed description of the differences, see the Zotero Installation Instructions.