LMS reporting status, explanation of options

Complete and Incomplete refer to the user's Completion status. In other words, did they finish the course or is it still in progress. 

Passed and Failed refer to the user's Success status. In other words, did they pass or fail a test.

This article provides more info about how Completion and Success statuses might be used by an LMS. The article is about choosing the status in Rise, but the same info applies to Storyline: 

• Rise 360: How to Report Completion and Success Statuses to an LMS - Articulate Support

Note that the article recommends using one of the options that begins with "Passed." However, you need to work directly with your LMS team to determine what option to use. For example, one of my clients required "Completed/Incomplete." 

You might also find this comment helpful (from a discussion that, unfortunately, is no longer available):

Here are the LMS reporting options we mostly use when publishing from Articulate for SumTotal LMS, and the scenarios for which we use them -

1. 1. Completed/Incomplete: We use this for any unscored content where we are tracking completion based on slide views. If the minimum number of slides are viewed, then the user is marked as completed. If not they are left in progress.
   2. Passed/Incomplete: We use this for scored content where we want the user to be left in progress if they do not achieve the minimum passing score. If the user achieves the minimum passing score they are marked as completed/passed with score, if not they remain in progress and no score is passed to SumTotal, allowing them to try again.
   3. Passed/Failed: We use this on a limited basis, primarily for things like compliance or certification activities where we want to record a failed status. If the user achieves the minimum passing score they are marked as completed/passed with score, if not they are marked as completed/failed with score. This is especially useful if you want to limit number of attempts through a learning activity for the purpose of assigning remedial training, etc., in the event of someone failing.

My guess is that these reporting options will function fairly similarly for any LMS.

I hope this helps.

Typically you can get some recommendations from your LMS provider.  Every LMS may have different preferences.