What is the "sensual desire" fetter?

Sensual desires (kāmacchanda) are thoughts expressing an intention to get sensual pleasures, from the six sense media (including mind). It's a hindrance.

Sensual lust (kāmarāga) is an underlying tendency or habitual obsession (anusaya) to seek sensual pleasures (AN 7.11). It's a fetter.

If one is still afflicted with the fetter of sensual lust (kāmarāga) due to not being fully liberated, then when careless attention (ayonisomanasikara) is applied due to lack of mindfulness (sati), the hindrance of sensual desires (kāmacchanda) will arise if not already arisen, and increase if already arisen.

If one is still afflicted with the fetter of sensual lust (kāmarāga) due to not being fully liberated, then when careful attention (yonisomanasikara) is applied due to the sustenance of mindfulness (sati), then the hindrance of sensual desires (kāmacchanda) will not arise, and if already arisen, it will be abandoned.

If one is no longer afflicted with the fetter of sensual lust (kāmarāga) due to being fully liberated, then careless attention (ayonisomanasikara) will never be applied due to a lack of mindfulness (sati), and so the hindrance of sensual desires (kāmacchanda) will never arise.

Bhikkhus, when one attends carelessly, unarisen sensual desire arises and arisen sensual desire increases and expands ...

When one attends carefully, bhikkhus, unarisen sensual desire does not arise and arisen sensual desire is abandoned.
SN 46.24

Bhikkhus, when the perception of impermanence is developed and cultivated, it eliminates all sensual lust, it eliminates all lust for existence, it eliminates all ignorance, it uproots all conceit ‘I am.’
SN 22.102

In DN 16, the Buddha talked about his discomforts of old age, simply to prepare his disciples for a future without his presence.

Furthermore, simply avoiding painful physical sensations do not necessarily indicate the arising of mental aversion. However, trying to distract oneself from painful sensations by actively seeking out pleasant sensations, or throwing tantrums, would be a sign of mental aversion. Also please see SN 36.6 (the arrow).

In my understanding, when used in the Buddhist technical sense, kamaraga and kamacchanda refer to two different things.

Kamacchanda is an active (current) desire, usually for a fairly specific object of material senses. For example, someone sees (or remembers) an attractive person (typically of the opposite gender) and experiences excitement, longing, and a desire for contact. That's kamacchanda. Technically it is based on a chain of associations that begins with grasping on a sign of beauty, a sign of pleasant taste, a sign of pleasant tactile experience etc. - i.e. a sign that promises a pleasant sensory experience.

Kamacchanda is abandoned by abandoning the clinging/sustenance of the chain of associations. In other words, by switching attention away from the sign and its connotations and inferences and the narrative they generate.

Kamaraga is deeper. It is the latent ever-present hunger for pleasure or fondness of enjoyment, in general. Its fundamental quality is "not having enough" or "not being at peace because of lacking something". Its root is the deep lying conviction that there must be something desirable in the world that can make one happy. This makes Kamaraga sort of the opposite of disenchantment, a somewhat romantic attitude to the world.

It is my guess that the two are related as the latent tendency and its active expression. Kamaraga underlies all instances of kamacchanda.

Kamaraga weakens with attainment of insight into the nature of true happiness, the peace that lacks any non-suchness. In other words, when one understands that nothing, no hypothetical pleasure, can possibly be better than the pleasure of being at peace now and not craving anything else. Kamaraga completely ceases with disenchantment, dispassion, etc. of Liberation.

As you can see, with these definitions Buddha's preference for peace and seclusion is not a kind of kamacchanda nor an expression of kamaraga. Why? Because it's not based on the idea of drawing pleasure from the (so-called) external world. When Buddha was leaving the Sangha he was not seeking or pursuing a source of pleasure or enjoyment, nor did he lack anything. The Buddha is the completely disenchanted one, by definition. He was simply abandoning the unhealthy environment for a more healthy one.

Another interesting question one might ask is whether this preference can be considered an example of aversion (to noise, quarrels etc.) but I'll leave that for another question.