Yes and yes.
Any way you slice it, it is state tax fraud, just like cheating on your state income or property taxes. You’re fraudulently structuring a transaction to avoid paying state taxes.
That being said, it is fairly common practice (maybe not standard) for local luxury goods retailers to ship goods to out-of-state addresses to avoid having to collect state sales tax (and sometimes retailers wishing to sail clearly beyond the line will send an empty box to the out-of-state address and allow the purchaser to walk out with the purchase).
This tax evasion can work because of a loophole in sales and use tax reporting, not a loophole in the law. As others have mentioned, most states have both a sales tax and a “compensating” use tax. The sales tax requires retailers selling products in state (or which have branches in state) to collect sales tax on sales of goods. Because states don’t have jurisdiction over businesses that don’t have branches in their states, they can’t require those businesses to collect sales tax for them, or even report purchases shipped to those states. As mentioned above, what constitues a branch for these purposes is the subject of dipute and litigation.
The use tax requires individuals (and businesses) who have purchased items out of state, but bring them into the state, to pay a tax on the goods they bring in equal to the amount of the sales tax they would have paid were the goods brought within the state. Where the individual has already paid an out-of-state sales tax on the purchase, the amount paid may be credited against the use tax owed (i.e. if you buy something in a state with a 3% tax and bring it into a state with a 5% tax, you only have to pay the 2% difference).
The problem with the use tax is that nobody keeps track of how most goods move across the states. An exception is things that need to be registered, like motor vehicles. If you try to re-register your car in another state, you can be sure the Motor Vehicle Department will be sure you’ve paid the appropriate sales/use tax on it before they issue a new registration. Otherwise, it is a bit of a free-for-all.
What this means is that if a retailer is asked to sell something to an out-of-state purchaser (who doesn’t live in a state where the retailer has a branch), the retailer can send it without collecting sales tax or reporting the sale to any state’s sales tax bureau. Assuming the retailer does this in good faith and without knowledge that the sale is being structured to avoid taxes (often a big assuming), the retailer has committed no tax violation. However, this pushes the tax compliance burden onto the purchaser (or recipient), who is required to pay use tax in the state where the goods are shipped, and if they are returned to the original state, use tax there.
So, if the Illinois purchaser who buys goods in Chicago but has them shipped to, say, Wisconsin, is committing Illinois sales tax fraud, Wisconsin use tax fraud, and Illinois sales tax fraud. If the retailer is complicit in this, the retailer is committing tax fraud as well. The friend who receives the goods is likely also criminally liable for fraud, or at least for accessory or conspiracy to commit fraud. Although fraud prosecutions are rare, particularly for the individuals involved (though they’ll make you pay the tax and perhaps interest and civil penalties if they catch you), you’ll sometimes hear about retailers getting busted for this type of sales tax fraud.