- Androids are humanoid robots, and they typically do not have organic parts. This rule is almost universal across all major franchises.
- Cyborgs have both organic and robotic components, with the organic components typically belonging to a human or humanoid, but the actual form of the cyborg is not necessarily humanoid itself. Cyborgs normally have an organic control system (brain)
- Bio-robots have both organic and robotic components, with the organic components typically belonging to a plant, animal, or other non-humanoid life form. Bio-robots normally have a computer control system.
- Replicant an artificial humanoid that is biological or indistinguishable from being biological.
Despite some conventional differences, both bio-robot and cyborg can be used synonymously. The differences are further muddied by terms like robo-animals, semi-organic robots, or a wide range of other terms used by various authors and settings.
While most of us can agree that a human with robot parts is a cyborg, and a robot with out living parts is an android, the T-800 (AKA: Cyberdyne Systems Model 101) from the Terminator Series seems to be the fringe case that people here don't agree about, because it is a robot grafted with human parts rather than the other way arround.
Many experts would argue it is a bio-robot because of the computer control system, but the Terminator movie itself disagrees:
He's not a man - a machine. A Terminator. A Cyberdyne Systems Model 101.
A machine? Like a robot?
Not a robot. A cyborg. A cybernetic organism.
Since this is scifi.se I would argue that cyborg is the right usage case for something like the T-800 due to its usage in canon, but on if this were biology.se, I would argue that bio-robot is the more correct term due to its usage in various real world contexts. In another setting like Warhammer 40k, something like a T-800 would more rightly be called a servitor or a semi-organic robot.
Another Fringe case are replicants. In the book "Do Androids Dream of Electric Sheep?" they called artificial humans Androids. However, in this case, the franchise latter changed the term to Replicants to avoid confusion when they produced the Blade Runner movies. Another similar case would be the Humanoid Cylons from the Battlestar Gallactica reboot. Here they addressed artificial humans as robots, replicants, or skin jobs despite being virtually indistinguishable from their organic counterparts. They only called the more obviously mechanical Cylons androids. So all in all, it seems the trend of the scifi community is to get away from using the term android to include biological robots, and use the term replicant instead.
Ultimately, these are all pretty new words in the English language, and their definitions and boundary are still fuzzy at best. Real world developments in cybernetics are also having retroactive impacts on the perception of these words. In court cases, arguments have been made about if everything from a person's pacemaker, removable prosthetics, or even cellphones should legally be considered part of their body or property with some claimants saying that all modern people are already cyborgs because we have become so reliant on computers to "function properly".