I think of
as being "behind" in space or order, whereas
is "back" as regards to position, movement or earlier in time.
But I am not a native speaker, so best to wait for a more qualified opinion.
Both words are used primarely as adverbs and signify "back, to the rear, behind,after." An example for "atrás" would be: "Ella quería dejar atras sus problemas." She wanted to leave her problems behind." An example for "detrás" would be: "La policía fue detrás del sospecho." The police went after the suspect.
One of the nuanced differences between the two is that "atrás" can be used as an interjection whereas "detras" generally is not used in this manner. For example: "¡Atrás!" Back! Back up! Additionally, another nuanced difference is that unlike "atrás", "detras" with "de" can be used as a preposition. For example, "La asistente del mago se escondió detrás de la cortina." The magician's assitant hid behind the curtain.