They're quite different. "Stereotype" is a fairly common word, "archetype" is fairly rare and specialized.
(Literally, the word "stereotype" once meant a printing process for making dozens of identical printing plates, but most people don't know that). Figuratively it carries the idea of lots of identical things.
Consider a person, or a culture, with prejudice against group X. Often, such people believe that all X's look alike--they can't recognize difference in faces. They may feel that all X's have the same behavior and characteristics. For example, all Scotsmen are stingy, all Swedes have blond hair, all Asians are good students.
The idea of a "stingy Scotsman" is a stereotype because it suggests that all Scotsmen are identical, as if produced by a stereotyping.
If you meet a Swede who actually has blond hair, you might say "he fits the stereotype."
If you express prejudice by saying "I don't want to hire any X's, they are all lazy," you are "stereotyping them."
"Archetype" isn't used when discussing prejudice. It doesn't mean "identical," it means "coming from a common or original pattern." For example, Owen Wister's 1902 novel, "The Virginian," was influential in shaping our image of the American "West." A lot of writers and moviemakers got their ideas from this book. We might say "'The Virginian' is the archetype of the 'western.'"
Like "Platonic ideal," "archetype" sometimes carries the mystical idea that the universe contains a grand pattern for everything.
"Archetype" is also a technical term invented by the psychologist Carl Jung. I don't know anything about Jungian psychology so I won't try to explain it. Read the Wikipedia article,
https://en.wikipedia.org/wiki/Jungian_archetypes and you will know more than I do. If someone is talking about Jungian archetypes, they will probably say so, or use the name "Jung," or it will be obvious that they are talking about psychology and the mind and the "collective unconscious."