You are correct regarding "sales" tax, but most, if not all, states with a sales tax also have an accompanying use tax for this very purpose. That use tax would apply to those things shipped to the consumer from out of state and used/consumed by the consumer. Under the use tax, the consumer is the one responsible for paying the tax to the state, not the seller.
Right. A “use tax” is almost completely unenforceable by the jurisdiction that imposes it, because there’s no way to prove that the person who buys an item from out of state is actually going to use it himself.