I was inclined to suggest that this was a general reference question, yet the answer wasn't obvious to me either! Here we go, in a variety of contexts, which is why the question is of interest to me too.
English usage and definition
Do purpose and reason mean the same thing?
To do something for a purpose means you're doing it to accomplish
something else, which is your PURPOSE. Accomplishing a purpose is only
one of many reasons why we do something--in this case, REASON is more
A reason can be trivial or illogical. One can purchase something for the reason that one likes how it looks e.g. I might buy sky-blue colored suede, open-toe, high-heel pumps because they're cute, but that won't accomplish the ultimate purpose in buying footwear, which is to facilitate walking.
The reason for which something is done, or the reason it is done in a particular way, is the purpose. Reason motivates action.
Purpose and reason are neither synonyms, nor antonyms, which was part of the question.
As a part of speech, both words are nouns. That is the similarity. This is the difference:
Purpose is the reason for which something is done or created or for
which something exists while Reason is a cause, explanation or
justification for an action or event.
Side bar: It is more appropriate to say "The reason for blah is blahblah". Usage is context-specific with "purpose" e.g. "The purpose of blah..." versus "The purpose for blah...".