Whether I'm using FTP or HTTP or SSH, can you tell me if there is software that I can install that will mask my IP during data transmission? How would this work if my IP address is assigned from my ISP, and presumably allows me to be tracked from the wall to their infrastructure? I also suspect this is different from simply proxying my request through another router (IP) like in TOR, or is it this same?
There is no piece of software you can run on your own machine that can mask, hide, disguise, or obfuscate your IP address when connecting to computers over the internet.
However, you can employ a proxy, such as Tor, an open proxy, or a private proxy to rebroadcast your traffic as theirs, effectively hiding your IP from the target. This would require proxy support in each application that you use (SOCKS5 is one common proxy protocol that you find in webbrowsers, for example). Your traffic will appear as the proxy's IP. Some sites block known proxies for this reason, and anyone that can get access to the proxy can find out your real IP address (such as police with a warrant).