There are obviously reasons beyond the light for this, but as you asked about light that is what I will comment on in this post.
There are a couple of aspects to this question. Easiest aspect to answer is that fish will reflect light differently according to the type of light. Light that is high in red for example will highlight red but other colours may be quite far removed from their true hue. Remember that we perceive colour only because the object is reflecting that colour, not because the object "is" that colour. And that has much to do with the light source illuminating the object. This is why water test colours should always be read in the exact same light to avoid misreading, and the best light for this is diffused daylight, not direct sunlight or artificial light.
Next we come to the light intensity, and this is a significant issue for fish. The brighter the overhead aquarium light, the less intense colour most fish will display. The reason is, that light stresses them. With a few exceptions, most aquarium fish species are forest fish; they may never see direct sunlight throughout their lives, depending upon their geographical situation. Forest canopy shades sun (and moon) light from reaching the water, or floating plants shade the water.
It is well known that most fish will display brighter colouration in dimmer light. This is one reason I advocate floating plants so often; this really is a very important aspect of proper fish keeping. Fish that do happen to live in water that is more brightly lit will tend to retreat from the brightly-lit waters, given the opportunity. It is no surprise that the fish in the brightly-lit watercourses are almost always found at the edge under overhanging vegetation, branches and outcrops, or floating vegetation. Baensch & Riehl (1987) called it a “light phobia” in characins. And it impacts the fish’s colouration too.
Fish (and amphibians) possess specialized cells called melanophores that contain hundreds of melanin-filled pigment granules, termed melanosomes. The sole function of these cells is pigment aggregation in the center of the cell or dispersion throughout the cytoplasm, thus altering the shade of colour. The melanophore cells are themselves light sensitive and respond directly to light by melanosome translocations, which is why the fish’s colouration pales during total darkness. Pencilfish in the genus Nannostomus have a diurnal patterning; at night the lateral lines break up into dashes, and the fish pales. This has been noted to occur even in blind fish, which shows that it is not sight that tells the fish it is getting dark, but the increase in darkness probably coupled with the circadian rhythm that sets in motion the natural response of the fish to darkness.
But the fish can also adjust the melanosomes voluntarily in response to environmental stimuli, stress, and social interactions. Fish in the store tank often appear pale, or after being netted and bagged will often be without any colour. Fish kept in brightly-lit tanks will frequently exhibit much less intense colouration. In all these cases, this “washed out” appearance is a natural response caused by high stress.
