AFAIK, all objects above 0K emit infrared radiation. It is an electromagnetic radiation, like visible light. I guess thermographic and infrared cameras work on the same principles, but their images are very different, the former is false color and very different from the visible image, the latter is black and white and usually correlates to the actual visible image, at least that's what I've seen so far. So physically, how exactly are they different?
At or around room temperature objects emit light in the far infrared. Cameras that detect this radiation generally give the false colour images that you describe. Because the camera sees radiation emitted by the objects no external source of light is required.
However a second type of camera operates in the near infrared and requires an external infrared light source to illuminate the field of view. These cameras give the black and white images you describe.
The near IR cameras have much higher image quality because the wavelength of the light is shorter and the intensity of the light is much higher. However it does mean carrying around a near IR light source to illuminate whatever it is you're trying to photograph. Wildlife documentaries tend to use near IR cameras because they give a good image of the wildlife but without scaring the animals by illuminating them with visible light.