Both terms have been used inconsistently and for describing wildly different things at different points in time over the last few decades. E.g., in the 80s and 90s, in the American political context, “neoliberal” described something different from the sense in which it’s being used today. It was meant to describe a strand of politics within the Democratic Party that was trying to take something of a "fresh approach" to New Deal liberalism, that shaved off some of the rough edges and made it less beholden to identity politics interest groups within the party. Within the context of the intramural fights within the Dem. Party in the 70s, 80s, and 90s, "neoliberalism" under this definition came to describe the "wine track" candidates like Gary Hart and Paul Tsongas, in contrast to the "beer track" candidates, who would appeal more to blue collar workers. It also described the views of many of the writers at The New Republic and The Washington Monthly, and there was a famous Charles Peters essay in The Washington Monthly titled "A Neoliberal's Manifesto":
http://coreyrobin.com/wp-content/uploads/2016/04/Charles-Peters-Neoliberalism.pdfBut now it’s mostly used as an epithet with a different meaning, and the definition seems to have become muddled:
http://nymag.com/daily/intelligencer/2017/07/how-neoliberalism-became-the-lefts-favorite-insult.html
