Question

The atomic number tells the number of what two items in an atom?

Answer 1

Well, `Z`, `"the atomic number"` gives (i), the number of protons, massive, fundamental positively charged nuclear particles.

Explanation:

And (ii), the number of electrons, fundamental negatively charged particles of negligible mass that are conceived to whizz about the nuclear core; of course electrical neutrality demands that `Z` and the number of electrons be equal.

`Z` determines the identity of the atom.........`Z=1,H; Z=2, He,,`
`Z=3, Li.............................Z=92, U`.

See

https://socratic.org/questions/why-do-all-isotopes-of-hydrogen-have-an-atomic-number-of-1#216989

for a description of `"isotopes"`, which are provide further details with respect to atomic structure.