Preprints are article versions that have not been peer reviewed by subject experts. This is a version before article has been submitted to a journal.
Postprint (author manuscript) is the article version accepted for publication. It is the version after journal submission that has undergone peer review (addressing comments from reviewers).
Final version includes all modifications, including the typesetting and is formatted according to the journal layout. It may be different from the postprint version.
Theoretically arXiv is primarily a preprint server. You should only post preprints to arXiv. Postprints should be posted in institutional or subject repositories, or on personal websites (if the copyright allows). However, there are many researchers who post a postprint to arXiv. this is not explicitely prohibited, as long as it does not violate copyright.