Interesting debate! As US collector and veteran, I rather enjoy observing that other collectors struggle with similar discussions. In the photo above, the cap the soldier is wearing is what is termed as a "Sun," "Hot Weather" or "Jungle" hat depending upon the MIL Spec and contract as well as the time period for which it was manufactured. My father, a Vietnam vet, still has his issued boonie and wears it when working around the yard in the hot sun. I have a few that I've collected from my veteran buddies who wore them in country (i.e. Somalia, Kuwait, and Iraq/Afghanistan).
Terminology is a funny thing. Within the same armed forces (I prefer that term), we can identify the same piece of equipment by a wide range of terms. It stands to reason, those varying names trickle out to the collectors spawning such lively debates.
Just my $.02.