Avogadro's number (6.022 x 10^23) represents the number of entities, whether atoms, molecules, ions, or any other particle, in one mole of a substance. It is a fundamental constant used in chemistry to relate the microscopic scale of individual particles to the macroscopic scale of bulk quantities.
When we say that a mole of a substance contains Avogadro's number of entities, it means that one mole of that substance contains 6.022 x 10^23 atoms, molecules, or particles, regardless of whether they are atoms or molecules.
For example, if you have one mole of oxygen gas (O2), it contains 6.022 x 10^23 molecules of oxygen. Each molecule of oxygen gas consists of two oxygen atoms, so you would have 2 * (6.022 x 10^23) = 1.2044 x 10^24 oxygen atoms in one mole of oxygen gas.
Similarly, if you have one mole of a pure element, such as carbon (C), it contains 6.022 x 10^23 atoms of carbon.
In summary, Avogadro's number is the same for both atoms and molecules because it represents the number of entities in one mole of a substance, regardless of whether those entities are atoms or molecules.