If the business you made the purchase from is in your state, or has storefronts within your state, you will be charged sales tax. As far as I know, if you buy from out of state, you are not charged sales tax from eithr state.
This has been my experience with every one of my online purchases of both firearms and other merchandise.
Look at gunbroker auctions. Right by the shipping costs disclosure line, there is a sales tax disclosure. It will say something along the lines of "Seller must collect sales tax, Tax rate is 7.00%, Tax must be collected from residents of: XX".
If the purchase is $300, and your FFL charges a $20 fee but your tax rate is 7%, you save a buck going thru a FFL but have to pay shipping costs. But you may be saving more than the shipping costs buying from Bud's or a similiar retailer than buying whatever from a local seller. Now, if you're buying a $1200 gun, a 7% tax is $84. Hard not to save money buying online in such a case.
(Plus, after about a half a dozen gun transfers or so, your FFL dealer may give you a break on the FFL transfer fee. Mine went from $20 per to $15 per and now I'm down to $10 per transfer.)