What is the Difference between Desire and Compulsion?

All 84,000 sections of the Dhamma are simply strategies for getting people to turn and look at the mind. The Buddha's teachings are many because people's defilements are many, and compulsions are one of the hardest to get rid of, as they are so deeply ingrained in us. To get rid of compulsions, that are very much a part of us, in having entertained them throughout our endless samsara, we have to be fully committed to this path. The path to enlightenment is not so easy. It is a path that goes against the stream. Buddha called this "Patisothagami " or going against the stream. It is just like when almost all the fish in the water are swimming with the flow while only one fish is trying hard to swim against the flow. It's not swimming against the resistance of the flow of water but also the resistance of the other fish that may impede its path.

Compulsion is a kind of desire that you have very little control of. The English word desire is a translation for either of two Pali words: tanha or chanda. Tanha means “thirst”. Tanha is a reflex, an instinct - the urge to grab and consume. Chanda can be said as “motivation.” This motivation can be either positive or negative. Chanda can refer to sense-appetites. The interest in Dhamma too is Chanda. The clear difference between chanda and tanha is that chanda is not a reflex, not an instinct and not a compulsion; it is a choice. And the main theme of Dhamma practice is to make the choices that undercut the power of instinct and compulsion. So in practice we use this positive kind of desire to undercut and eradicate the negative type of desire.

There are a range of skills, techniques and strategies in Dhamma to get rid of the compulsions type of tanha (thirst). Once we break through its hold on our lives, our mind can finally come to rest.

In Buddhism, there are wholesome/skillful & unwholesome/unskillful desires.

Unwholesome desires are called 'craving' or 'tanha', which are the 'compulsion' referred to.

Now this, bhikkhus, is the noble truth of the origin of suffering: it is this craving which leads to new becoming, accompanied by delight and lust, seeking delight here and there; that is, craving for sensual pleasures, craving to be, craving not-to-be.

SN 56.11

'Craving' or 'compulsion' (namely the 'lust', 'resistance' & 'ignorance' quoted below) is shown by a lack of self-control, enslavement ('fettered') & the final result of suffering when not getting or losing the object of compulsion.

It is similar with an untaught worldling: when touched by a painful (bodily) feeling, he worries and grieves, he laments, beats his breast, weeps and is distraught. So he experiences two kinds of feeling: a bodily and a mental feeling.

Having been touched by that painful feeling, he resists (and resents) it. Then in him who so resists (and resents) that painful feeling, an underlying tendency of resistance against that painful feeling comes to underlie (his mind). Under the impact of that painful feeling he then proceeds to enjoy sensual happiness. And why does he do so? An untaught worldling, O monks, does not know of any other escape from painful feelings except the enjoyment of sensual happiness. Then in him who enjoys sensual happiness, an underlying tendency to lust for pleasant feelings comes to underlie (his mind). He does not know, according to facts, the arising and ending of these feelings, nor the gratification, the danger and the escape, connected with these feelings. In him who lacks that knowledge, an underlying tendency to ignorance as to neutral feelings comes to underlie (his mind). When he experiences a pleasant feeling, a painful feeling or a neutral feeling, he feels it as one fettered by it. Such a one, O monks, is called an untaught worldling who is fettered by birth, by old age, by death, by sorrow, lamentation, pain, grief and despair. He is fettered by suffering, this I declare.

SN 36.6

Both are same qualitatively but quantitatively different. Compulsion is a strong desire which cannot be mitigated easily. Your instincts (unconscious mind) are 9/10th of you and your conscious mind is 1/10th. If you do not have sex for few months then desire will take form of compulsion. Desires especially sex, food, and social if repressed for long ends up in compulsions of various sorts. Read Sigmund Freud to understand how mental disorders originates through subjugation of id by ego.

Please refrain from liking and disliking sex or any other animal activities which is part and parcel of being human. Just watch yourself. If you are becoming hyper about food, sex etc maybe it is the lifestyle, food etc which is at fault. Just watch yourself and it will be revealed to you.