The difference between atoms and molecules is one of seeing from within and from outside. Atoms are the smallest part of matter which may or may not possess all of its properties. Molecules, on the other hand, are smallest units having independent existence and possessing all its properties. Certain molecules are formed by the combination of atoms of different elements, while some others are formed by the union of atoms of the same element. Atoms are conserved across chemical transformations, and molecules can come in and go out of existence.
On a finer note, atoms and molecules can be easily distinguished with the help of atomic absorption spectroscopy. Absorption spectra of atoms consist of isolated very narrow bands or sharp lines, whereas molecules exhibit series of closely spaced broadened bands.