Indeed, the lens colour of Fire fighting cameras is often the grey colour from the hard carbon coating.
I do not know why the colour of the AR coatings varies. I assumed it was different batches of lenses and that as the coating is applied, minor differences in the process effects the colour, bit not the AR performance. As stated, some lenses have several bands of differing colours on them. This is, of course, in the visible light domain and, as we know, that means nothing in the Longwave energy domain.
As a side note, Hard Carbon coatings are known as "diamond like" coatings due to their resistance to scratching. That are not indestructible though ! They should be treated with care like any optical coating.
Sadly lenses that are subjected to long term damp contions can suffer degradation of their AR coatings. Hard Carbon coatings are no different. The damage is a form of corrosion and is seen as spider lined under the coating, white corrosion breaking through the coating, lifting of the coating or mottling of the coating surface. In the case of lifting, the coating can flake off in whole areas, it can rub off easily if cleaned or it becomes loose crazing all over the lens that can easily rub off if touched.
Loss of the AR coating is bad news for Germanium Lenses as it directly effects the transmission of the lens. The lens will still function, but with reduced performance.
Keep your lenses dry !
Fraser