When using a WSAPI query from the Object Model, you are using the login credentials that you have logged into Rally with. It is also possible to have accessed the Object Model using BASIC credentials if you were not logged into Rally.
If you are using Postman with an API key, that API key may not belong to the user ID that you log into Rally with, however it may belong to another user.
If this is the case, then the two user accounts may not be assigned the same resources within Rally and the ResultCounts will differ.
Resolution is to use an API key that belongs to the same user account that you are logging into Rally with.