There aren't really special tags for private posts.
You chose from the normal thread tags that are available at the time of creation and then mark it private and select whom you want to participate.
Think of private threads more like messages or emails directly between a specific set of people.
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Six Demon BagJack Burton: Hey, what more can a guy ask for?
Egg Shen: Oh, a six-demon bag!
Jack Burton: Terrific, a six-demon bag. Sensational. What's in it, Egg?
Egg Shen: Wind, fire, all that kind of thing!