First, Some Definitions...

FTP
File Transfer Protocol. A familiar and older method of transferring files to/from a server. Usernames, passwords, and data were not encrypted. Examples include older versions of WsFTP and DOS ftp.exe.

FTPS
File Transfer Protocol over SSL. Increased security of FTP by adding SSL encryption to the data transferred. It did not encrypt the username and password however.

SSL
Secure Socket Layer. By using an SSL certificate and key file an encrypted connection can be established between the client (such as a browser or FTP client) and a server (such as a web server or file server). Since the connection is encrypted, the information transmitted back and forth cannot be "read" as plain text by outside parties.

FTPeS
File Transfer Protocol Extended over SSL. This expansion increased security of FTPS by adding SSL encryption to the username and password during login, as well as the data transferred. All communication between the client and server was now encrypted.

SFTP
Secure shell File Transfer Protocol. Uses a stronger and more secure encryption method based on public/private key pairs. All traffic, including login, between the client and server is encrypted using SSH public/private keys. SFTP builds upon the connectivity provided by SSH.

SSh
Secure Shell. Connects a client computer to a server computer using public/private keys. All communication between the two computers is encrypted using these keys. In its basic form, it is much like a DOS command prompt, allowing the user to enter commands on the command line, yet do so on a remote server. It also facilitates encrypted file transfers between the two computers.

SFTP Client
An application like FileZilla, PuTTYscp, WinSCP, CyberDuck, SecureFX, or latest versions of DreamWeaver. You use it to connect via the SSh encrypted protocol to a server. For ease of use it typically mimics the behavior of the older and familiar FTP clients.

Pulic Key
The unique key you can give out to others so they can put it on their server to allow you to connect.

Private Key
The unique key you keep and never give to anyone else. It is also the key you will configure your SFTP client to use.