This is what's going on here.
The difference between atoms and ions in that context comes from the nature of the chemical substance that you're dealing with.
In other words
#"covalent compounds " -> " NO ions " = " atoms"#
#"ionic compounds " -> " ions"#
For example, calcium chloride is an ionic compound that contains calcium cations,
#"CaCl"_2 -> "Ca"^(2+) + 2"Cl"^(-)#
Notice that each formula unit of calcium chloride contains a total of
You thus have
#"2 moles Cl"^(-)/"1 mole CaCl"_2" "#and #" " "3 moles ions"/"1 mole CaCl"_2#
as conversion factors to use when converting from moles of calcium chloride to moles of chloride anions or moles of ions (calcium cations and chloride anions).
Since you won't find any calcium and chlorine atoms in this substance, you will refer to them as calcium cations and chloride anions, i.e. as ions.
In this case, you say that each molecule of nitrogen dioxide contains
Your conversion factor here will be
#"3 moles atoms"/"1 mole NO"_2#
because every mole of nitrogen dioxide contains
So remember, the nature of the chemical substance tells you if you should use atoms or ions.