Time warping from ancient Rome to the recent past... Several years ago I took some notes from https://www.ncbi.nlm.nih.gov/pmc/articles/P…58/#!po=31.0811; here are some select quotations:
“From sensory pleasures and drugs of abuse to monetary, aesthetic and musical delights, all pleasures seem to involve the same hedonic brain systems, even when linked to anticipation and memory. Pleasures important to happiness, such as socializing with friends, and related traits of positive hedonic mood are thus all likely to draw upon the same neurobiological roots that evolved for sensory pleasures.”
“We note the rewarding properties for all pleasures are likely to be generated by hedonic brain circuits that are distinct from the mediation of other features of the same events (for example, sensory, cognitive) (Kringelbach 2005). Thus, pleasure is never merely a sensation or a thought, but is instead an additional hedonic gloss generated by the brain via dedicated systems (Frijda 2010).”
“Identification of hedonic substrates has been advanced by recognizing that pleasure or “liking” is but one component in the larger composite psychological process of reward, which also involves “wanting” and “learning” components (Smith et al. 2010).”
“In conclusion, so far as positive affect contributes to happiness, then considerable progress has been made in understanding the neurobiology of pleasure in ways that might be relevant. For example, we can imagine several possibilities to relate happiness to particular hedonic psychological processes discussed above. Thus, one way to conceive of hedonic happiness is as "liking” without “wanting.” That is, a state of pleasure without disruptive desires, a state of contentment (Kringelbach 2009). Another possibility is that moderate “wanting,” matched to positive “liking,” facilitates engagement with the world. A little incentive salience may add zest to the perception of life and perhaps even promote the construction of meaning, just as in some patients therapeutic deep brain stimulation may help lift the veil of depression by making life events more appealing. However, too much “wanting” can readily spiral into maladaptive patterns such as addiction, and is a direct route to great unhappiness. Finally, happiness of course springs not from any single component but from the interplay of higher pleasures, positive appraisals of life meaning and social connectedness, all combined and merged by interaction between the brain’s default networks and pleasure networks. Achieving the right hedonic balance in such ways may be crucial to keep one not just ticking over but actually happy.” [I cringe at the use of "higher" pleasures, but overall, I'm seeing a distinction between pleasure networks and wanting (desire) networks.]
So I gather that the pleasure/pain network is separate from wanting (desire), but that they are integrally intertwined. This makes sense in light of our difficulty in determining whether desire is pain. It also reinforces the idea of desires not being the same as pleasure/pain when considered in regard to the categories of desires.
Another way to look at this might be that ice cream and desire both can lead to pleasure/pain, but neither are pleasures or pains. Ice cream and desire are different types of things from pleasure/pain, as well as from each other.