Since the early days of SSH, file transfers have been supported through a command called SCP. This command simply copies a specific file between remote computers. It provides no other file operations such as listing, deleting, and renaming. These operations were done using the native OS commands on the remote computer. Thus the commands required would vary depending on the OS of the remote computer. This presented a problem when trying to automate file transfers either through scripting or GUIs. SFTP was developed as a solution to this problem. The names of the commands were probably modeled on the FTP commands (e.g. get and put), but that is as far as the similarity with FTP goes.
The SFTP protocol was designed to be carried by SSH, and most SSH servers support SFTP.
You can download a free trial of CompleteFTP, a Windows SFTP server, from this link.