One theory is that apes only evolved from monkeys in Asia, and then spread back to Africa where they diverged into gorillas, chimp species, and hominids. This theory is supported by the fact that "lesser" apes, the gibbons and siamangs, are only found in Asia.

As for how they travelled, it doesn't take much geologic time for a species to spread across a continent at the rate of a mile a year. Getting to Africa is thought to be a freak one-time occurrence of monkeys accidentally rafting across on tree wreckage.

As for body similarities, primates are noted for the behavioral diversity instead of large diversity in body structure. Their behavioral diversity and complexity is the key to their success.