Well, if we stick to the original 'robot' meaning 'slave', we rule out cyborgs - like people with pacemakers, who are emphatically not part of a slave class.
But that would be boring, so let's get some new ideas!
Villano is referring to 'synthezoids', IIRC. I would class these as androids, robots that look like people. The android classification can be subdivided, however. It includes Threepio, the T-100 and T-1000, Replicants, synthezoids, Alien-verse androids, Red Dwarf waxworks, Twiggy of Buck Rogers infamy, most of the villains from Masamune Shirow's Dominion: Tank Police, and a bunch of others. Thus, it may be profitable to use two categories when classifying robots: shape, and operating principles.
'Shape' is the most apparent. Thus, we can neatly categorise our artificial friends. Off the top of my head, there are:
- androids (subcategory: nekoids, cat-girls used as pleasure slaves)
- canoids (not only prevalent in science fiction, but now in homes around the world with products like Aibo and some of those ridiculously cute-yet-scary robot fluffballs they're selling today)
- mobile pocketknives (Star Wars astromechs such as Artoo, and modern bomb disposal droids)
- appliances (KITT of Knight Rider is a good example, and I might make a case for your PC being one too)
- nanites (which may assemble into larger networks, but need their own category for the base state)
- titans (big robots with weapons, often somewhat humanoid but not to the extent of being true androids)
- shapeshifters (such as the T-1000, which has no base shape, and also including nanite networks)
- transformers (fundamentally different to shapeshifters, appliances, and titans, but combining characteristics of all three)
- modern power suits (read John Ringo's Posleen War saga and see if you agree with my categorisation of them as robots)
- traditional mecha (the big, impractical but cool things we all know and love)
- zoid mecha (big, less impractical mecha mostly based on low, predatory hull designs for increased military effectiveness)
- smart munitions (bullets and missiles with their own guidance systems and onboard decision-making processes - very low-end robots, with limited lifespan, but robots nonetheless)
- smartships (spaceships with no crew requirement, sometimes bordering on smart munitions, sometimes altogether more sinister like the HAL-9000)
- cyberspace entities (the paperclip in MS Office is a robot, believe it or not, up to certain recent incarnations of Megaman and Shodan)
- cyborg attachments (cybernetics is, properly, communications; people who communicate information between man and machine by thought rather than interface, and thus the common cyborg, one who communicates movement data to artificial limbs)
Then there are the various Operating Principles:
- mechanoids (running on basic mechanical principles - pistons, hydraulics, electric or fuelled engines, etc; single nanites count as mechanoids, biologicals, or syntho-biologicals, depending on the way they function and their complexity)
- psychodroids (a term I made up just now to describe mechanical systems that function Just Because - systems that are so complex they're not properly understood and thus produce lifelike results while still being based on fully-understood sciences; positronic brains are a good example)
- biologicals (normally genetically engineered life forms or gelfs, and normally androids; some may be able to reproduce, some may be assembled off-the-shelf and not reproduce)
- syntho-biologicals (presumably like Bishop from Aliens - creatures with systems that replicate organic functionality without being grown from previous organic systems)
- nanocolonies (nanites forming a larger whole - T-1000 counts, but other models may be closer to synthos and not as malleable)
- field effects (robots formed of energy itself, or some other exotic thing like those electron atoms I read about years ago - like the Terminator in T3, which I haven't seen)
- virtuals (computer programs - pretty much exclusively for cyberspatial entities above, and dividable into programmed entities and emergent entities that aren't realy robots at all, like the Puppet Master)
Then you can combine operating principles to create hybrid models. The T-100, for example, is a mechanoid core with a biological shell; from what I've seen of Evangelion, something like the inverse of that is true of the EVA mecha; what's-her-name from Alien Resurrection was a syntho-organic with a virtual interface; IIRC ornithopters from Dune are zoid mecha with a mechanical body but biological wing flappers, etc.
If anyone can think of other, truly different categories, be my guest and contribute them!