Right now I'm using Costco's partnership with Elavon for credit card processing that also includes debit cards, and it's been a while so I don't think there's anything terribly different about accepting them. It's the same old industry that wants to charge you those transaction fees (that's at least kind of reasonable, you know?..) on top of $185972398742134 in monthly fees for everything from renting equipment to account fees and minimum charges and what have you. I think I went this way because it was cheaper than an Authorize.net+whatever mess (for brick and mortar, mind you) and better than the fees others wanted, on top of my spotting the brochure while shopping at Costco.
> ...update from the real world.
All things considered, I don't think there's anything fundamentally different about physical purchases vs. online purchases made with a credit card. The only big one is that micropayment systems and fees aren't really in place for brick and mortar retailers that might struggle just to accept cards in the first place, whereas it's becoming more and more common online because people are buying 99 cent songs and apps all over the place. It needs to happen for the former because people make 99 cent purchases everyday anyway (usually combined with something else, or else they're paying with cash...hopefully), but that's a problem that hasn't even been sufficiently solved in an all-digital world that loves the idea but can't easily do it because of all the damn fees.