In our atmosphere and in our homes convection is a key heat transfer mechanism.
But, if you have ever broiled anything in your oven, radiation is the main mechanism. If you have ever stood by a campfire and felt the heat of the flames on your hands, that is radiation, the sun, as I mentioned in my first post is radiation.
No, vacuum cannot transfer heat via conduction or convection the only heat transfer mechanism which works through a vacuum is radiation. This is why we have vacuum thermos bottles, this is why you have double pane windows. Double pane windows are to close together to allow convection currents to develop so the only mechanism allowed is radiation, for small temperature differentials radiation is not able to transfer very much heat.
Convection heating implies currents in some fluid, be it air or water, radiation does not require a medium, just like light does not need a medium. But then light is a prime example of radiative energy transfer. The mechanism for radiative heat transfer is Electro Magnetism, and that may be best for you way to differentiate between convection and radiation. Convection is heat transfer via currents in a fluid, radiation is heat transfer through electromagnetic interactions ONLY.