What do oxygen atoms and oxide ions have in common? 

As far as we are aware, an atom, compound, or molecule's ion is not the same as the substance's natural state. So, ions may arise by solvent dissolution or external energy application. The process of obtaining or losing electrons might create the ion.

As is well known, an oxygen atom, which is found in oxygen gas, is located on the right side of the periodic table. In this state, sometimes referred to as the oxidation state, there is no charge.
When oxygen is separated from any chemical, an oxidising ion is created. The octet is completed by the addition of two electrons, as shown by the symbol O^2-.
Let's look at the choices.
Option  (A) Oxygen atom and oxide ion cannot have the same size since oxygen has only eight electrons and eight protons. However, the oxide ion is created by adding two more electrons to the oxygen atom, which causes the oxygen atom's electrons to repel one another, increasing the size of the oxide ion.

As we have seen in the discussion above, the oxygen atom and oxide ion cannot both have the same amount of electrons. Therefore, choice (B) is equally incorrect.
The oxygen atom and oxide ion's electrical configuration is as follows:

$O=1s^{2}2s^{2}2p^4$
$O^{2-}=1s^{2}2s^{2}2p^6$

Therefore, the option (C) is also not correct.