I looked at her like she'd just asked me if I had two eyes.
Of course a cyborg is part human. That's what a cyborg is! But at that point I realized not everyone is as nerdy as I am, and also, general media uses these terms interchangeably and often, incorrectly, so here are the very basic breakdowns.
Cyborg: a being that is both manufactured and organic. One of my favorite examples...Darth Vader. He is a cyborg. Part man. Part machine. Technically, so is an old guy with a pacemaker. Think about that for a second.
Android: an android is a completely mechanical being made to look and act like a human. Because I am such a dork, and I use Star Wars repeatedly for my examples, think C-3PO.
Robot: a completely mechanical entity that may or may not look human. Ie, an android is a robot, but a robot is not always an android. For my last Star Wars example, our little R2D2 is a robot, but not an android, so calling it a droid is technically incorrect assuming that's short for android. (But we'll forgive George Lucas for his genius.)
So to recap with pictures...