I've seen a lot of arguments about it and the only conclusion I can draw is that nobody knows what neoliberalism is. Some people will tell you it's Reagan and Thatcher style trickle-down, with "liberal" in this case being the 1800s sense and the idea being it's a revival of minimal-intervention economics. Other people will tell you it's Obama and Clinton center/center-left capitalism, with "liberal" here being the American definition, and the "neo" referring to the idea that this is the hip, modern style of liberalism. I've seen one guy claim it was the recurring thread between Clinton, Reagan, Lincoln, and Genghis Khan. For some reason, people in the former camp avoid the term and use the second definition in a derogatory fashion; people in the second camp seem to either have no real opinion on the topic or have a thing about "reclaiming" the term, usually to refer to their own position in a positive manner. I think the last guy was joking, but you can never be sure.
The split definitely arises from the American definition of "liberal", though. The Clinton definition seems to have arisen from people being unaware of the European definition when they heard the word "neoliberal".