stoichiometry - Does a stoichiometric coefficient represent molecules or moles of a substance?

I understand that the one mole of atoms is equal to $6.02\times10^{23}$ atoms. However, when I used various resources to learn about stoichiometry, they showed me a balanced equation:

$$\ce{2H2O->2H2 + O2}$$

and said "2 moles of water" decomposed to form "2 moles of molecular hydrogen" and "1 mole of molecular oxygen". It is my understanding that there are only 2 molecules of water, not $2 \times 6.02 \times 10^{23}$ molecules of water and so on with the other parts of the equation as well. Could someone please clear up my confusion?