Neo liberalism is the core ideology of modern conservatism. For example, both the republican and democrat parties in the United States adhere to Neo Liberal ideology. They are both conservative.

Neo liberalism is the ideology of deregulated capitalism. Neo liberalism holds that everything should be marketable without government interference, including healthcare, real estate, power generation, water, etc. Pioneered by Margaret Thatcher and Ronald Reagan, it is the dominant political ideology across Western democracies. Liberals and Conservatives are both adherents of Neo Liberal capitalist ideology. Leftists are those who support regulation, they are definitionally anti-capitalist. When people refer to the democrat party as socialist or democrats as Leftists, they're just misusing those terms. Democrats are Neo liberal conservatives who, by and large, support deregulated capitalism.