They are not the same, but they have the same numerical values.
Thus, the mass of one C-12 atom is 12 Da, and the mass of one mole of C-12 atoms is 12 u.
The molecular mass of H₂ is 2.016 Da, and the molar mass of H₂ is 2.016 g.
People speak carelessly when they say that molecular mass and molar mass are the same.
They really mean that the molecular and molar masses have the same numerical values but different units.
The statement in the above image is WRONG.