I will disagree with Robusto and Mr. Disappointment insomuch that the two words have very different meanings. This is copied from my local dictionary and I think it describes the difference well:
While prototype and archetype are often used interchangeably, they really mean quite different things. An archetype is a perfect and unchanging form that existing things or people can approach but never duplicate (: the archetype of a mother), while a prototype is an early, usually unrefined version of something that later versions reflect but may depart from (: a prototype for a hydrogen-fueled car).
In other words, a prototype is a (usually physical) draft. An archetype is an ideal example or theoretical perfect form. Something could correctly be labeled both a prototype and archetype but generally prototypes are inferior to the final product. Their very label of prototype implies that it will be replaced with a different form later in the design process.
The final prototype can be considered the primary modeling example if the object is intended for mass production and a loose usage of "archetype" could apply. Then the meaning would shift from focusing on the prototype and, instead, focusing on the reproductions. As in, the reproductions better faithfully mimic the archetype because if they didn't than the process is flawed. This usage holds no implications about the perfection of the archetype and, therefore, I consider prototype the appropriate word.
Even the other dictionary examples posted in the other examples are not suggesting they are synonyms:
prototype - a first or primitive form
archetype - original pattern from which copies are made
"First form" and "original pattern" are similar but their usages are drastically different.
archetype - an original model or type after which other similar things are patterned; a prototype
Using "prototype" to describe "archetype" works but the usage example helps reveals the difference:
"'Frankenstein' ... 'Dracula' ... 'Dr. Jekyll and Mr. Hyde' ... the archetypes that have influenced all subsequent horror stories" (New York Times).
"Prototype" would be incorrect in that sentence. Here is the same dictionary's definition of prototype:
prototype - an original type, form, or instance serving as a basis or standard for later stages.
The difference in meaning is again hard to see but prototype is a staged type or form: It is "original" in the sense that it came before the next one in sequence. "Archetype" is "original" in the sense that there wasn't anything else before it. You can (and usually do) have a sequence of prototypes; you generally only have one archetype.
The meanings are similar:
Optimal: Best or most favorable; optimum
Ideal: Satisfying one's conception of what is perfect; most suitable
In my mind optimal is the best that is reasonably possible while ideal is the perfect and possibly unattainable.
Best Answer
The term archetype may refer to an ideal, but not necessarily so. The American Heritage Dictionary gives this definition and example as its first:
An archetype can be a model of excellence, but also a model of evil. Ideal almost always suggests something positive.
Merriam–Webster’s first definition is:
In this case, perfect indicates most exact, not necessarily good.
Prototype is actually closer to archetype. While they are often interchangeable, prototype is more often used for inanimate objects. Archetype is usually used when referring to living things or characteristics of living things, although the earliest uses may have been for objects. See for example the Online Etymology Dictionary.
Note that this source (and others) also describes a specific use of archetype in Jungian psychology, referring to an inherited idea or mode of thought derived from the experience of the race and present in the unconscious of the individual.