No, there are actually two types of HIV: HIV-1 and HIV-2, and they have slightly different origins.
HIV-1 is closely related to the strain of SIV found in chimps. While HIV-2 is closely related to the strain of SIV found in sooty mangabeys monkeys. The crossover of HIV-2 to humans is believed to have happened in a similar way as HIV-1 (by eating monkey meat).
HIV-2 is far more rare, and less infectious than HIV-1, so it infects far fewer people. It is mainly found in a few West African countries, such as Mali, Mauritania, Nigeria and Sierra Leone.
To complicate things further, HIV is also classified by four main groups of viral strain (M, N, O and P), each of which has different genetic make-up. HIV-1 Group M is the strain that has caused the majority of HIV infections in the world today, meaning it is the dominant strain.