# Definition of relative atomic mass

I found out there are two definitions of relative atomic mass $A_\mathrm r$.
First definition is $A_\mathrm r$ is the mass of 1 atom of an element relative to 1/12 the mass of carbon-12 atom. It can be found in any chemistry school textbook.
Second definition is what I just found and dont understand. It states $A_\mathrm r$ is the mass of 1 mole of atoms relative to 1 mole of carbon-12 atoms.
Can you kindly explain second definition with examples?

$$\frac{\text{mass of one atom}}{\frac1{12}\text{ mass of one atom of }\ce{^12C}}\\=\frac{\text{mass of one atom}\times N_\mathrm{A}}{\frac1{12}\text{ mass of one atom of }\ce{^12C}\times N_\mathrm{A}}\\=\frac{\text{mass of one mole of substance}}{\frac1{12}\text{ mass of one mole of }\ce{^12C}}$$