Zotero Online is a web application that takes the majority of the functionality of Zotero 7 and condenses it for use on Chrome, Safari, or Firefox. The same version of Zotero Online works on all computers; there is no separate version for different browsers or for PC vs Mac. It lacks the full functionality of the desktop version, but can be used in tandem with it, or alone for simple tasks.
Use Zotero Online if:
Go to the Zotero Website. Click the option "register for a free account." Once you finish, you may have to confirm your account through an email message. Login, and now you can see your library and get started!
Connectors allow your web browser to save citations to your Zotero library. Open your preferred browser and click the Zotero Connector to install. Each browser has its own version of the Zotero Connector; so, you will need to install multiple versions of Zotero Connector if you use multiple browsers.
Unlike Zotero Online, Zotero 7 runs as a separate program instead of part of your web browser. You can have both Zotero 7 and Zotero Online and use both on the same computer.
Use Zotero 7 if:
Word processor plugins allow you to insert citations and bibliographies directly into your documents. These plugins should install automatically when you install Zotero 7; so long as you close Word before you complete the installation. You can check the Word Processor Plugins page for advice if the plugins did not install.
Zotero 7 can be used with Google Docs- just make sure you have the Connector installed, and then when Zotero 7 is running you can find the Zotero menu in the toolbar to cite while you write.