Liberal can refer to social beliefs or economic beliefs.

In terms of social beliefs, liberals promote equal rights and oppose discrimination based on identity. As I understand it, this definition arose from the economic definition based on a comparison of the laissez-faire market approach to the laissez-faire identity approach. (Note: Social liberalism does not refer to liberal social beliefs as commonly expressed in the US, it’s an actual political platform which includes economic aspects.)

In terms of economic beliefs, liberals support free markets as well as the right of the individual to private property including that of the means of production. They oppose government intervention and unions, and support low taxes, privatization, and deregulation. This is the basis of liberal political platforms in the US.

Progressives are not radically economic liberals because they support a greater amount of government intervention. Additionally, economic liberals consider the ability to accumulate private property as the basis of liberty, whereas progressives tend to believe that liberty is created when there is a lack of oppression. They support strong social safety nets in order to prevent the disadvantaged from being entirely exploited. This aspect of progressivism is where it differentiates itself from the more liberal part of the party.

So progressives are less liberal than Third Way Democrats, not more. What they are more of, is libertarian. Liberals believe the right to oppress is freedom, libertarians are the ones who believe the right to not be oppressed is freedom. (Classical libertarianism == Anarchy.)

Most progressives do not provide an alternative to liberal economics. They want to make the game more fair with less downside, but they are still capitalists and the point of capitalism is the accumulation of resources held by increasingly few hands so as to enable increasingly more capital intensive ventures. Traditionally this inequality is considered a form of hierarchy and oppression by libertarians, which is the basis for their opposition to private property and capitalism. So progressive politicians have libertarian elements but the capitalist basis of their platform puts them further into liberal territory.

Neoliberalism is essentially an extension of market theory and commodification into parts of life and society that which previously did not have markets / were not commodified. Things like social relations, love, happiness, right to travel, and atmospheric carbon can be quantified, and so a market can be made for them in order to commercialize and extract profit from them.

Liberal economics has a strange history. Adam Smith is often credited as the founder, but he was a philosopher who wrote a critique of capitalism. Later on, economists realized that he had laid out the blueprints for how to make money from the economy. So instead of viewing it as a critique, they saw it as a playbook. Adam Smith was actually supportive of intervention in order to limit the harms of capitalism. Some liberal economists hang onto the concept of limits and regulation, while another area that differentiates neoliberals is that they tend to be even stronger / more radical proponents of deregulation, austerity, and minimized government spending.