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It's different everywhere. In NY, if we trade in a car on a purchase of a new car (not a lease), we are only taxed on the difference between the value of the trade-in and the agreed upon price of the new car, not the full price of the new car.. So you save a fair amount of tax on the new car. If instead you sold the car privately, then take that cash and put it down on the new car, you pay tax on the full agreed upon price of the new car. And in the meantime, whoever bought the used car privately gets to go pay sales tax on that too (despite the fact that you already did when it was new).
Here, the buyer is always the one paying tax though. So to your question, if autotrader said its worth 35k, that's not including sales tax that the buyer would pay.
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