They're different, but both aiming to achieve the same end result. You can download a demo version of Capture (which works for 90 minutes and then needs to be restarted, and doesn't allow you to save) to see if you like it - http://www.capturesweden.com/
CITP stands for "Controller Interface Transport Protocol" - it's an Ethernet based "protocol" that allows consoles to talk to visualisers etc. It was originally developed by the team at Capture, but it open for anyone to use. There is more info here: http://www.citp-protocol.org/
Yes, that should be easy. Phantom ZerOS uses networks setup through Windows, so to change IP addresses etc, you do this through Windows, and then just select the IP address in Phantom. If using the same laptop, you can choose the 127.0.0.1 IP address.