It depends on the software. If you are talking about an FTP client on your own computer what happens in that scenario is that they download to your computer and upload to the destination server. In effect, it's not really going from one ftp server to the other, it's going to your client first.
Alternately you can just connect directly. Since you've spoken about cpanel servers in other topics I'm assuming you are using linux so try doing this:
Log on to one of the servers though command line.
Type "ftp" and press enter
Type "open hostname.com" and press enter
It should prompt you for username and password etc, and then you can use ftp commands to do everything over command line.
If you want more information, just search for ftp commands and you'll find plenty of sites describing command-line methods of using ftp.