A ferrofluid is just a fluid with suspended particles of magnetic material (e.g. iron), coated with a surfactant so that the particles themselves cannot aggregate together. The fluid itself can be just ordinary water. Because the suspended particles can be magnetized in the presence of a local magnetic field, they will exert forces on the fluid they are suspended in. Thus, the fluid will essentially behave as though it were a magnetic liquid, which of course it isn't - it's a non-magnetic liquid carrying a suspension of solid magnetic particles. No, it's not a magnetic polymer.

Ferrofluids are fluids that will react to a magnetic field. They aren't magnetic in the same way as a bar magnet, though. First, let me describe how a ferrofluid is made. The magnetic material in a ferrofluid isn't actually a liquid - it's a bunch of nano-sized (really, really tiny) particles suspended in a liquid. The particles aren't magnetic on their own - they wouldn't stick to your refrigerator if you put them next to it. The particles are what we call "paramagnetic". This means that if we place a magnet next to them, the magnetic field will cause the particles to become polarized. Basically what this means is that the magnetic field turns the particles into little tiny magnets that will then move around within the magnetic field, much like iron filings on a sheet of paper. They won't stick to metal like a normal magnet, but they will react with already made magnets.

Other materials will react in a similar way. Some materials are what we call ferromagnetic - they can become permanent magnets, and "emit" their own magnetic field. These are the normal magnets you would see in every day life. Other materials are what we call paramagnetic - they only become magnets once they are in the presence of a magnetic field. However, most magnetic materials we encounter in everyday life are just normal solids, so they don't display the cool looking shapes of ferrofluids.

Many materials have properties similar to ferrofluids, minus the fluid behavior. For example, aluminum is sometimes considered a paramagnet. This is why a magnet will stick to your refrigerator (which has an aluminum casing usually), but a normal piece of metal will not. It's not a permanent magnet - it only displays magnetic behavior when in the presence of a magnet field.

I'm unfamiliar with magnetic shape changing polymers, but I would suspect that these would basically be like ferrofluids, assuming they're suspended in some liquid. If you're talking about just a polymer sitting on it's own like some sort of plastic or Styrofoam that will change it's shape in a magnetic field, then that probably wouldn't be considered ferro-fluidic, since it's not really a fluid, but rather an elastic solid. However, it is still probably displaying paramagnetic behavior, so it would be very similar to a very fluid.