I've had some good 50/50 shirts as well as cotton so I'd say that it depends on the brand. Some people are pretty definitive about wanting 100% cotton so, there's that too. There was another thread about this in the forums somewhere, and there was a good bit of advice about just setting your customers expectations correctly up front, so they know what they are getting - no surprises.
As far as what things are called, you might check out a t-shirt site like Hanes or American Apparel and see what they are calling things. If you want shirts that stop more at the hip, you might be looking at Junior sizes?
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