No, parsley and basil are not the same herbs, but they do have some similar properties, which is why basil works so well as a parsley substitute.
For a start, parsley and basil have completely different origins. Basil is native to India, while parsley originates from Europe and Western Asia.
As you might expect, given their differing origins, these two herbs are also members of different plant species. The botanical name for parsley is Petroselinum crispum. Petroselinum is a genus of the Apiaceae family.
Basil, meanwhile, is called Ocimum basilicum in scientific terms and is a member of the Lamiaceae family.
While both families are flowering plants known for their aromatic properties, Lamiaceae are generally classified as types of mint, while Apiaceae are known as Umbellifers.
Therefore, while parsley and basil are similar in some respects, the existing system of plant classification shows that they are not the same.
Moreover, the difference between parsley and basil is quite marked when it comes to taste. While they can be substituted for one another with decent results, depending on the type of dish, parsley is much earthier and more bitter than basil.