There are three primary versions of a manuscript:
Pre-print – A pre-print is the original version of the manuscript as it is submitted to a journal. The pre-print has not been through a process of peer review. It typically looks like a term paper - a double spaced .doc file with minimal formatting. (Highly recommended: Include link to publisher’s version)
Post-Print – A post-print is a document that has been through the peer review process and has incorporated reviewer’s comments. It is the final version of the paper before it is sent off to the journal for publication. It may be missing a final copyedit (if the journal still does that) and won't be formatted to look like the journal. It still looks like the double spaced .doc file. Sometimes, the term "pre-print" is used interchangeably with "post-print," but when it comes to permissions issues, it is important to clarify which version of a manuscript is being discussed. (Highly recommended: Include link to publisher’s version)
Publisher’s version - This is the version of record that is published on the publisher’s website. It will look quite spiffy, having been professionally typeset by the publisher. Library databases will link to this version of the paper.
Generally speaking, publishers are more likely to be okay with authors posting copies of post-print versus other manuscript versions. But each journal is different, and authors need to be aware of what they can do. The copyright transfer agreement is the best place to find this information.
If you no longer have your copyright transfer agreement, or if you are checking into your rights before you publish (good for you, btw), you can check SHERPA/RoMEO to find out what you are allowed to do with your paper.