Before going to the whole discussion, let us define the terms. Permanence refers to how well a printed image lasts over time, whether it fades when exposed to sunlight, heat, or airborne pollutants. Durability refers to how well the image resists accidents, such as spilled water, smudging and fingernail scratches. Sometimes, the distinction between the permanence and durability becomes difficult to make, as the very definition of ‘accident’ depends on the assumptions and the expected mode of use. Thus, for outdoor signage, the images are exposed to water (rain, fog, snow) all the time. Even for photographs in a gallery, the images can get an occasional exposure to water due to saliva drops if people passing by.
Archivability on the other hand is the ability of a printed material to be stored for a long time without exposure to light or airflow. Other precautions also can be taken during this storage, such as keeping the relative humidity and temperature low, etc. Again, many other things can happen during the storage of an archived documents, for example, the pages can stick together, the paper itself can yellow and disintegrate, etc. We will be ignoring those.
Early inkjet photographs
After early inkjet photographs started to take on photo printing market in the end of 1980s-early 1990s, it was quickly realized that the photos do not produce a very durable/permanent output. It took about 20 years and now we fully enjoy durable and permanent photos, as the technology has matured. Also, inkjet output became good enough for the outdoor exposure. The latter is now getting more attention, and the image permanence of photos becomes less significant, as most of the images are now stored digitally and printed only when needed!