Technically, the .org is only supposed to be used by non-profit organizations, but that restriction is unlikely to be enforced.
The domain will work the same as any other domain. When you buy a .com, your registrar tries to sell you the same domain on most of the other TLDs (some actually do require certification and are enforced, but not .org). My employer has .com, .net, and .org for its primary domain and the .org has always just forwarded to the .com. Wikipedia, on the other hand, does the exact opposite.
Still, you might want to avoid using the .org for a business just to avoid confusion. All your customers will try to go to the .com, and in the worst-case scenario, whoever owns the .com could pursue legal action against you for trademark infringement. This happened to my small business when our shortened .com domain (we owned long and short versions of the domain) coincidentally differed from another company's domain by only one character. Even though the other company only owned a trademark on the graphic design of their logo, our lawyer said we only had at best a 50/50 chance of winning if we chose to fight. To me it sounded like they were abusing a loophole in the system, but our lawyer said the court's determination would be based primarily on "likelihood of confusion" and not on the distinction between word marks vs. design marks. If you are in a completely different industry and sell different products from the .com site, you might be able to get away with using the .org, but that also is no guarantee.