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That will depend on whether or not you have actually been discharged. In most cases, when dealing with the reserves, they do just separate you. However, in some rare circumstances they will place you on an AWOL roster.
The only real way to make this determination is to file for your records with the national archives. If they have separated you, any record of your separation would be contained in that file.
You would make this request by filing an SF Form 180.