In general, there's no law that requires companies to honor an advertised price if that price is wrong. Typographical errors, miscommunication and other glitches can result in items being offered at what appear to be deep discounts – discounts that would be ruinous for the company if it were forced to honor them.
The simple answer is yes they can charge different amounts if you buy online as oppsoed to going to the store. Often running an online shop will have lower costs and therefore goods can be sold at a lower price. As such, if a different price is charged online this should be made clear to consumers.