Arduino Uno R3 and R3 SMD

There is no difference (other than the fact that the SMD chip has two more pins, but I don't think the Uno SMD breaks those out). There are - however - clone boards on the market that use a different serial chip, the CH340G - and the drivers for that are not included with the IDE (google will get them for you in a jiffy) - the CH340G works fine once the correct drivers are installed. There are also boards with counterfeit FT232R's on them that don't work unless you jump through hoops with the driver now (google ftdigate for details) - though most of these are out of circulation now.

Since you haven't described the symptom of the problem, we can't venture a guess on why your board didn't work.

The shortage of DIP atmegas was quite a while in the past. Many of the Uno clones use the SMD chip now simply for cost reasons (usually when something on the board fails, it's not the '328p, but the 16u2 used as serial adapter - so the socket is less useful than one might hope. At least on official boards with the 16u2 - the CH340G seems less liable to fail under abuse than the 16u2).