robots - 100% mechanical, no organic or living parts
androids - robots that are designed to look human-like (100% mechanical)
cyborgs - organic/living thing with added mechanical or cybernetic parts
Robot
Android
Cyborg
And just to complete the list of frequently misapplied terms:
Bionic refers to any mechanical system that deliberately imitates the functionality of a biological one, regardless of whether it visually resembles a biological system.
Cybernetics refers to a class of control mechanisms, not to the mechanical parts themselves. In the specific context of robotics, any device that provides real-time sensory feedback to a human controller can accurately be described as “cybernetic”, regardless of whether it’s implanted in (or, indeed, even physically attached to) its controller.
The title of this post was actually the punchline of a localized joke in FLCL