SIV works in much of the same way in monkeys, i.e. they rarely die from it, even though they may have high viral loads. However, in some species of monkeys (non human primate in general), SIV will evolve into AIDS and kill the host. Like HIV there are different strains of SIV, i.e. SIVsmm (sooty mangabeys) and SIVcpz (chimps). These two strains lead to HIV-1 (from chimps), which is the most common variant of HIV and HIV-2 (from mangabeys), which is rare and isolated to a few countries in Africa, even though it has popped up in Western countries in low numbers.
In regard to the above mentioned theory, the most probably cause of HIV is called the "Bustmeat theory." Essentially it is believed that SIV jumped to humans in the early 1900's due to the common practice in most African nations of hunting monkeys and then eating the meat. If a hunter was scratched, bitten, or exposed to the blood of a monkey with SIV, he/she was exposed to SIV, which over time evolved into HIV in humans.
My only problem with that theory is that SIV is believed to have been around for the past 32K-11K years and humans have been hunting monkeys and such for far longer than that. IMO SIV had to have made the jump sooner into HIV.