An inductor is not a resistor, idiot.
Carbon film? Sure you don't mean carbon comp? Not many carbon films around much more. Nearly none at 1%. Probably more expensive than hugely mass produced metal film versions as well.
Carbon comps are different than metal films as well. They have Bakelite overclad bodies (or epoxy). They are all brown. It is how they are made, not how they are coated. Most are not coated. They get value stripes painted on, and that's about it.
Examples of what? They are not painted (metal films), they are covered in an epoxy type paint/dip/cladding. Very similar but thinner than that which a disc capacitor is dipped into to seal it away from the environment. When heated, it discolors, so choosing a light color (blue) that turns darker is better than choosing a dark epoxy color like tan or brown, or dark blue, and not being able to distinguish thermal damage as readily. I have seen brand differences that range from a very light blue all the way through nearly green turquoise, but all were light colors such that the stripes would be the most readily visible.
It is probably very similar to "Stycast" thermal epoxy formulations. Probably a good reason why we do not see caps and resistors being clad in white epoxy. I do not know what it is, but it would likely be composition related, because that or a light gray would also be good choices. I have seen old mil parts that were light gray. It will show dark or light print if the right shade is chosen.
To put it simply... It is not an indicator of the type or process by which the resistor was made, it is an indicator of a maker that had enough common sense to choose a good background color for his epoxy dip, and nothing more.