Is Shakyamuni Buddha Siddhartha Gautama?

This is very similar to https://buddhism.stackexchange.com/questions/22696/did-siddhartha-gautama-achieve-nirvana It is also kinda separate/different, and since I have not "realised all phenomena are non-self" I might ask my own question, especially as I am more interested in Mahayana Buddhism, just not what 'nothing to attain' means. Is our historical Tripitaka Buddha also Siddhartha Gautama, the prince who left home? Clearly they are not identical, because the latter has undergone complete and perfect enlightenment (so not the same question as the above). But are they in any sense the same? Follow up questions like whether the Jataka stories are about Shakyamuni Buddha, whether the dharmakaya is Shakyamuni Buddha, would also be appreciated.