The FileSystemEntry interface of the File and Directory Entries API represents a single in a file system. The entry can be a file or a directory (directories are represented by the DirectoryEntry interface. It includes methods for working with files—including copying, moving, removing, and reading files—as well as information about a file it points to—including the file name and its path from the root to the entry.
The FileSystemFileEntry interface of the File System API represents a file in a file system. It offers properties describing the file's attributes, as well as methods for creating a FileWriter object to write to the file or a File object to read the file.
The original File System API was created to let browsers implement support for accessing a sandboxed virtual file system on the user's storage device. Work to standardize the specification was abandoned back in 2012, but by that point, Google Chrome included its own implementation of the API. Over time, a number of popular sites and Web applications came to use it, often without providing any means of falling back to standard APIs or even checking to be sure the API is available before using it. Mozilla instead opted to implement other APIs which can be used to solve many of the same problems, such as IndexedDB; see the blog post Why no FileSystem API in Firefox? for more insights.