I don’t see neoliberalism as vague as at all, but I certainly wouldn’t be surprised if many folks feel that they have a cloudy or murky understanding of it, though. And, for that, I certainly don’t blame them. In my opinion it refers to classical liberalism, what they refer to as economic liberalism in this definition.

Additionally, just the opening few paragraphs of the Wikipedia on neoliberalism do a good job of describing it withal:

Neoliberalism is a form of economic liberalism, which advocates – under reference to neoclassical economic theory – support for great economic liberalization, privatization, free trade, open markets, deregulation, and reductions in government spending in order to enhance the role of the private sector in the economy.

Neoliberalism was an economic philosophy that emerged among European liberal scholars in the 1930s attempting to trace a so-called ‘Third’ or ‘Middle Way’ between the conflicting philosophies of classical liberalism and collectivist central planning. The impetus for this development arose from a desire to avoid repeating the economic failures of the early 1930s which conventional wisdom of the time tended to blame on unfettered capitalism. In the decades that followed, neoliberal theory tended to be at variance with the more laissez-faire doctrine of classical liberalism and promoted instead a market economy under the guidance and rules of a strong state, a model which came to be known as the social market economy.

In the 1960s, usage of the term “neoliberal” heavily declined. When the term was reintroduced in the 1980s in connection with Augusto Pinochet’s economic reforms in Chile, the usage of the term had shifted. It had not only become a term with negative connotations employed principally by critics of market reform, but it also had shifted in meaning from a moderate form of liberalism to a more radical and laissez-faire capitalist set of ideas. Scholars now tended to associate it with the theories of economists Friedrich Hayek and Milton Friedman. Once the new meaning of neoliberalism was established as a common usage among Spanish-speaking scholars, it diffused directly into the English-language study of political economy.The term neoliberal is now used mainly by those who are critical of legislative initiatives that push for free trade, deregulation, enhanced privatization, and an overall reduction in government control of the economy.

American scholar Robert W. McChesney notes that the term neoliberalism, which he defines as “capitalism with the gloves off,” is largely unknown by the general public, especially in the United States. Today the term is mostly used as a general condemnation of economic liberalization policies and their advocates.

People who use it to refer solely/mainly to Democrats, as if it’s the other side of neoconservatism or something are wrong! Bill Clinton, Barack Obama and George W. Bush are all neoliberals. I can’t think of a current Western leader that is not a neoliberal, in fact! Ed Miliband has talked some populist talk/rhetoric; however, I don’t expect that he’ll actually go through with any of it, though, should he ever actually become (the United Kingdom’s 55th) and the next prime minister.