HIV is a retrovirus, meaning it inserts its genetic code into the host cells. So not only do those cells make the virus, but all their descendants will, as well. This makes HIV almost impossible to eradicate from the host.

We have drug treatments for leishmaniasis which are extremely effective, and once it’s out of your body, it’s gone for good. With HIV, we have treatments that can inhibit the virus’s spread inside the body, but the infect cells and their progeny are still infected, and will remain so for decades. If the treatment is stopped, the infection will resume in full force.

So basically, leishmaniasis is easily curable in most cases, but HIV is not.