The Edit Offline action lets you download an item to your computer so you can edit it there. This locks the item in the library to prevent others from editing the item simultaneously. It's available for every content item.
The Edit Online action lets you edit the content item without first saving it offline. It's available only for Microsoft Office 2003 or greater files.
The Inline Edit action lets you edit plain text, HTML, or XML documents directly in the document library. It's available for these content types, which can all be created with the Create Content feature in the library.
The Edit in Google Docs action lets you work with items in Google Docs. Like the Edit Offline action, this locks the item in the library while it is being edited. It's available for supported document, presentation, and spreadsheet formats.