What you say is correct of what is commonly referred to as Type 2 HIV, which is also most commonly found within Africa. There is also another main type, known as Type 1, which is more commonly found within North America. While both major versions of it carry pretty well the same complications, there are actually some variances between the two major types. In fact, it's even possible (as I know someone with it) to be infected with both types at the same time. Unlike 2 strains of the same type, both types can survive independently of one another.
Also, the more common pre-AIDS name that the disease carried was commonly referred to as GRID (Gay Related Infection Disease), at least within North America for some time….
Lastly, I want to point out one point of technicality. Although it is common thought that HIV is required to constitute AIDS, do not fool yourself. Technically, the CDC does not require the presence of HIV to constitute AIDS.... By technical medical definition according to the CDC, AIDS is nothing more than a CD4 count that has dropped below 200, regardless of the presence of HIV. That being said though, HIV itself is what makes things much more interesting once the CD4 count drops below 200, which is why it is regarded in such a manner that one requires the other, despite the technical difference.
I just thought I'd point that out in case it's of any use or value to you..... Aside from those couple of minor things, yes.... You are correct. 