Terminal App: What comes after connection?
secure shell, ssh, is a command line based method of talking to another computer. By default, there is no graphical interface associated with ssh.

Speed

The speed of your upload is probably limited by your Internet connection. The protocol used to transfer the files will make a difference but it may not be significant.

Domestic quality Internet connections tend to have much slower upload speeds than download speeds. This is particularly true for ADSL based connections. VDSL, cable, and fibre connections offer faster upload speeds.

Try running a speed test on your Internet connection. What values do you see? Is the upload number much lower than the download?

If you are transfering thousands of small files, an alternative protocol is probably worth trying. If you are transferring tens or low hundreds of larger files, ftp will likely go as fast as any other method.

Command Line - rsync

From your question, it sounds like you have ssh access to your server. This is great. If you are comfortable with the command line, you can use a tool like remote sync, rsync, to perform the file transfer. See Fastest and safest way to copy massive data from one external drive to another for more about this approach. With rsync you will end up issuing a command something like:

rsync -rv --progress '~/Pictures/My Photos/' user@sftp.server.com:~/Pictures/


Alternative command line tools to rsync include scp.

Graphical Interface - CyberDuck

Alternatively, consider using a tool like CyberDuck to connect to and securely transfer files to your server. Try using the same server address as with ftp but instead use sftp; note the addition of an s. This stands for secure. sftp will give you a File Transfer Protocol (FTP) connection over a secure connection, much like ssh.