An arthi is a person who prays to God only when he is in trouble. An artharthi is one who prays to God not only when he is in trouble but also when he wants things. A jignasu seeks to understand what is God, but that doesn’t mean he doesn’t have a desire or he will not pray to fulfil his desire nor will he not pray when he is in a soup. Therefore, he’s basically a jignasu and he has desires as well.
You have to see these three states as a plus, one adding to the other. So the artharthi includes the arthi but becomes something more, the jignasu includes the artharthi and the arthi but he is something more. The jnani , however, shouldn’t be compared to these three. In fact, Krishna himself says, `Treat the jnani as myself because he has discovered his identity as me.’ But, yes, at times a jnani may pray for the welfare of the world, for the welfare of his students, and at times he may have a desire—a desire to reach out to more people. The Vedas are full of prayers of wise people who prayed like this. A wise person may actually pray, `May a lot of students come to me and benefit from this knowledge’.
In the case of the first three, the desires are more or less binding in nature, their happiness depends on the fulfilment of the desires. In the case of the jnani, the desires are not binding. His happiness is not compromised whether the desire is fulfilled or not because he has discovered that the source of ananda is himself.