What is the difference between saying “ $ 1 $ mol of nitrogen atoms” and “ $ 1 $ mol of nitrogen molecules”?

Hint: Moles which alternatively known as mol is the standard scientific unit used in chemistry for measuring larger quantities of very small particles like atoms or molecules or any other specific particles. Moles are especially assigned an extremely large number of units, $ 6.02214076 \times {10^{23}} $ .
 $ mass\;of\;substance = atomic\;mass \times number\;of\;moles $ .

Complete answer:
To answer this question we have to first know about the atoms and molecules of the matter. Atoms are the fundamental unit of matter. It cannot exist independently, they exist in a combined state. Molecules are formed when two or more atoms combine with each other. It exists independently in fact it is the smallest particle to exist independently.
In this question, we have to differentiate between nitrogen atoms and nitrogen molecules. A molecule of nitrogen is made of two atoms of nitrogen that means it is twice of the nitrogen atom. We know that the atomic mass of the nitrogen atom is $ 14 $ .
Mass of nitrogen atom = $ atomic\;mass \times number\;of\;moles $
Thus, the mass of nitrogen is :
 $ \Rightarrow 1 \times 14g $
This is equal to $ 14g $ .
Now as we discussed above, a nitrogen molecule contains two atoms. So the molecular mass of nitrogen will be:
  $ \Rightarrow 2 \times 14 = 28 $
So the mass of nitrogen molecule will be:
 $ \Rightarrow 1 \times 28g $
This is equal to $ 28g $ .
From this it is clear that the mass of a nitrogen molecule is twice the mass of a nitrogen atom.

Note:
Previously, the definition of mole is that the number of atoms which are determined experimentally, to be found in $ 12\;gm $ of $ carbon - 12 $ . The number of units in a mole is also termed as Avogadro’s number or Avogadro’s constant.