Bonobos evolved from the common chimp, about 2 million years ago. Bonobos used to be classified as a subspecies of the common chimp but they are now generally accepted as a different species. They don't have the same relationship as lions have with tigers, because the closest relative of lions is the Jaguar, and the next closest relative is the leopard. In fact, it seemed likely that the lion evolved from the leopard, and the jaguar then evolved from the American subspecies of the lion. Tigers OTOH, are most closely related to the snow leopard, and they too probably evolved from the leopard but long before the lion did.
Bonobos are geographically isolated from the chimp and the gorilla by the Congo River. Since chimps and gorillas cannot swim, they have not been able to go to the same places bonobos live. If they can, the bonobo will likely be driven to extinction because they are smaller than the chimp and they are not as territorial as chimps. Gorillas in fact keep chimps from the territories with brute force, so bonobos would be no match for a gorilla.
Because gorillas and chimps are not found in the bonobo's territory, the bonobo has the monopoly on the best habitat they can find. They spend a lot less time looking for food everyday than the chimp as a result, and they don't have to hunt monkeys and lower primates to supplement their diet. Bonobos are also less territorial than chimps and they do not fight each other over territory. Male bonobos are also smaller and less powerful than chimps. Unlike chimps, which lived in troops ruled by males, bonobos are dominated by females, and they band together as a group and they use sex as a weapon against males. Males that do not behave themselves and who try to dominate females are denied sex. Bonobos also have sex everyday, and they have it with anyone, because they have so much time on their hands.
Because of these differences, scientists reason that the bonobo should be classified as a different species, because if they ever meet again with chimps, their distinctiveness will likely disappear, because they will likely be driven out of their territories. Further, bonobo females will likely not mate with male chimps because they don't like bullies, and female chimps may not like to mate with male bonobos either because female chimps often mate with males that offer them meat, and bonobo males have no meat to give since they do not hunt. Of course all of these are speculation, but since they are geographically separated from one another, it is the best we can do, when we have to determine whether they will or will not interbreed with one another if they do meet. Because scientists theorized that they are not likely to be able to interbreed, they are considered different species based on the Biological Species Concept.
Lions too will not interbreed with tigers even though both species are found in the same part of India. It is one reason lions and tigers are classified as different species.