In literature, what is the difference between an archetype and a motif? They seem very similar, thus I was wondering if there is any distinguishable difference between the two.
Motif is a recurring element within a story, while archetype brings in elements based on what we know or expect.
A motif is a recurring element or theme within a story. For instance, I just finished a book about the Hindu god Krishna and there are recurring elements in there about how Krishna is able to do all this amazingly cool stuff because people have faith in him. So the motif could be said to be "faith is power".
Archetype is the bringing in of elements that are similar to what we know or expect. For instance, Krishna does archetypically god-like things, like kills demons, builds a city in a day, and drives a horseless chariot. The city is archetypically a god-made city because it is roofed with precious stones and the streets are gold, there are fine statues and fountains everywhere, etc.
Stating it a different way, let's say I want to write a story about Robin Hood - the motif would be "rob from the rich and give to the poor" - so Robin and his band of Merry Men would steal from the Sheriff of Nottingham and give money to the poor families in the district. In that story, Robin gets captured and thrown into the dungeon. I would describe that dungeon using archetypes related to dungeons - chains, torture devices, dank, cold, dark, etc.