nuclear and atomic energy is it the same?

Answer 1

Yup

Answer 2

In practice, yes, but what everyone refers to is more correctly called nuclear energy. "Atomic energy" is incorrect. "Noo-kyu-ler" is even more incorrect; it's pronounced "noo-klee-er."

atomic => entire element, including electrons
nuclear => nucleus of the atom, i.e., protons and neutrons

So atomic energy would deal with the whole atom, which would have to include the electrons. Nuclear energy would only deal with the nucleus.
What everyone means by atomic/nuclear energy is energy from disrupting or merging nuclei (plural of nucleus), so nuclear energy.

It was originally referred to as atomic energy back in the 1940-60's, because people didn't know any better. Now they do.