To pretty much everything you stated in your question, "no".
That convection requires a medium is not the main difference, it is simply the most obvious aspect of what is a fundamentally different mechanism for transferring energy. Convection is the transfer of energy by movement of a medium, whereas radiation is the transfer of energy by, well, thermal radiation. Conduction also requires a medium, but, again, it is a fundamentally different mechanism than either convection or radiation; in this case it is the transfer of energy through a medium.
Unfortunately, analogies are hard but if you can visualize the particles involved, it would help. Picture the red hot iron you mentioned. On a molecular level, the material is emitting lots and lots of photons (hence why it is glowing red). The creation of these photons takes energy; energy from the heat of the iron. These photons leave the iron, pass through the environment, and eventually collide with some other object where they are absorbed and deposit their energy. This is radiative heat transfer. If that energy is deposited on your retina or a CCD (like in a digital camera), an image forms over time. This is how infrared goggles work and they would work equally well in high vacuum as here on earth.
In conduction, the next simplest example, there is no generation of photons (physics nerds forgive me for the sake of simplicity). The individual atoms in the object are vibrating with heat energy. As each atom gains energy from its more energetic neighbors, so it gives up energy to its less energetic ones. Over time, the heat "travels" through the object.
In convection, the molecules of gas near the object gain energy, like in the conduction case, but those same molecules that gained energy then travel through the environment to some other location where they then give off their heat energy.
In summary:
- radiation = generated and absorbed photons
- conduction = molecules exciting their neighbors successively
- convection = molecules heated like in conduction, but then move to another location
Three processes are involved:
Conduction: Heat flows from the object to its environment. Removal rate of heat from the interface further away from the object is proportional to the coefficient of conductivity (0.024 for air, 205 for aluminum -see http://www.engineeringtoolbox.com/thermal-conductivity-d_429.html).
Convection: The interface between the object and air is the same, but removal of heat from the interface is by replacing the interface volume, due to the flow of air (e.g: due to wind). Convection is more effective than conduction within the air - hence the familiar habit of blowing on hot food to cool it.
Radiation does not depend on the immediate environment. There is, however, a balance between incoming radiation (from the sun, earth, space etc.) and outgoing radiation (from the object). With very hot objects - radiation heat transfer would be dominant.
Best Answer
The phenomenon of convective heat transfer occurs as a result of a combination of fluid deformation (movement) and conduction within the moving fluid. The fluid deformation physically brings hotter fluid into contact with cooler fluid to enhance the rate of conductive heat transfer between these regions. In many cases, this occurs in close vicinity to a boundary, and is modeled using a convective heat transfer coefficient to calculate the heat flux at the boundary. If there is a boundary between two fluids, and both fluids are moving/deforming/shearing, then there can be convective heat transfer on both sides of the boundary, within each of the fluids. In this type of situation, these is a convective heat transfer coefficient applicable to each side of the interface.