Mole concept and molar mass

The mole is the SI unit for amount of substance: one mole is the amount of substance that contains exactly as many elementary entities — atoms, molecules, ions, or any other specified particles — as there are atoms in exactly 12 g of the carbon-12 isotope. This fixed number of entities is the Avogadro constant, $N_A = 6.022 \times 10^{23}$ per mole, and it is the same number no matter what is being counted: one mole of electrons, one mole of water molecules and one mole of sodium atoms all contain $6.022 \times 10^{23}$ entities.

To connect this particle count to a mass that can be weighed, chemistry defines the atomic mass unit (u) as exactly one-twelfth the mass of a single carbon-12 atom. Because most elements occur naturally as a mixture of isotopes, the atomic mass quoted for an element is really an average atomic mass, weighted by each isotope's natural abundance — carbon's atomic mass of 12.011 u reflects the small natural share of heavier $^{13}\mathrm{C}$ and $^{14}\mathrm{C}$ alongside the dominant $^{12}\mathrm{C}$. Molecular mass is the sum of the atomic masses of every atom in one molecule (water, $\mathrm{H_2O}$, is $2(1.008) + 16.00 = 18.02$ u); for ionic solids such as $\mathrm{NaCl}$, which do not exist as discrete molecules, this same sum is called the formula mass instead.

Molar mass is the mass in grams of one mole of a substance, and it is numerically equal to the atomic, molecular or formula mass expressed in u — so water's molar mass is 18.02 grams per mole and $\mathrm{NaCl}$'s is 58.5 grams per mole. This equivalence is what makes the mole useful at the bench: it converts a particle count into a mass on a balance through $n = \dfrac{m}{M}$ (given mass over molar mass) and $n = \dfrac{N}{N_A}$ (number of entities over Avogadro's number). Gases add a third route: at STP, one mole of any ideal gas occupies close to the same fixed molar volume, so $n = \dfrac{V}{V_m}$ also holds.

The recurring NEET trap is assuming that equal masses of two different substances must contain equal numbers of particles. They don't — Avogadro's law guarantees equal numbers of particles only for equal moles, and mass converts to moles only after dividing by molar mass. So equal masses of, say, $\mathrm{H_2}$ and $\mathrm{O_2}$ contain wildly different numbers of molecules, because their molar masses differ; any question comparing number of molecules or number of atoms between two given masses must be routed through $n = m/M$ first, and only then multiplied by $N_A$ — never compared as masses directly.