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Bob DeRosierBob DeRosier 

Difference between custom fields for object by API call & retrieve object with version 38

Custom field didn't show up when - was skipped  (Roster_Fields_to_Hide) using the API.
    Exact same field in 2 diff obj - ref same global value set, same name, etc.  One was a custom object (Registration) and the a Standard Object (Contacts).  The field appeared in the custom object, not the standard.

To test whether it was a problem of two fields with same name in different objects, we added Roster_Fields_to_Hide1 to Contacts object and neither  of the two fields came down using the API.  
check the FLS on the profile of the api user - from your description I would assume you have read access to the field on the standard object but not to the field on the custom object