I think that both exist in our speaker systems.
Absolutely. Most systems generate suprisingly high levels of IMD - basically it is a result of non-linearities in the system performance. An amp will not perform exactly in the same way when delivering 1 Amp of current as it does when delivering 1 milliamp. A speaker driver will not behave exactly the same way at the center of its travel when compared to sticking out one quarter of an inch and at its maximum Xmax of excursion (linear operating range where non-linearities are less than a terrible 10%). Therefore when amp and speaker cone are oscillating from one extreme to another (as it plays your favorite big band or rock tune) it causes intermodulation on the delicate voice of the vocalist - "the camera shake affects the photo" analogy.
IMD is rarely caused by speaker placement or the room. Most of what the room does (reflections) is an entirely linear effect and will not create any new frequencies. Only if things get loud enough to rattle and vibrate surfaces can a room or objects in the room create completely new frequencies not on the recording. This is when the vibrating surfaces add their own sounds. Typically these things will not go away with changing speaker placement or listening position...whereas an extra screw in the drywall or blutak tightening the catch on a cabinet door may help.