Desires imply cognition and rational decision-making, whereas pleasure and pain are sensations which we can't decide not to feel.
This needs a bit more parsing: I don't think that there's always a rational component to desires. In fact a large part of advertising is finding ways to create desires which get beneath the rational. Choosing whether or not to act on a desire is definitely a rational operation, but on some level a desire is a craving, a feeling, perhaps a type of pain.
From Oxford Languages Dictionary online:
de·sire /dəˈzī(ə)r/ noun
a strong feeling of wanting to have something or wishing for something to happen.
"a desire to work in the dirt with your bare hands"