SOHO is located at the Sun-Earth L1 point, effectively the same position as the Earth in the diagram above.

All three of these spacecraft have coronagraphs. These are telescopes equipped with an occulting disk to block out the Sun, making an artificial eclipse that allows the camera to see fainter phenomena. Those fainter phenomena can be related to the Sun (like coronal mass ejections, for instance) or they may be background stars. Once in a while, moving objects like planets and comets wander into the coronagraph fields of view. (For more on what a coronagraph is and how it works, visit spaceweather.com.)

Now compare the positions of the STEREO and SOHO spacecraft in the diagram above to this little animation of ISON's orbit, which I made using JPL's neato orbit diagram viewer. It's basically the same perspective as above, looking down on the solar system from the north. The light blue part of ISON's orbit is above the plane of Earth's orbit. The dark blue part is below the plane. You can see that STEREO Behind was viewing the comet coming almost straight-on, while STEREO Ahead was viewing it almost exactly from the side. That produced major differences in the comet's appearance to the two spacecraft. SOHO had a more oblique view than either of the others.