Dan has noted on his blog that Progessives are not necessarily Socialists, and I’ve heard other liberals mention that they are tired of being called Socialists. I don’t really blame them, and I think Dan is right in that the two groups, Progressives and Socialists, are not necessarily the same. Even though I believe that Progressives can have socialist ideas.
Wikipedia defines Socialism as
Socialism refers to a broad array of doctrines or political movements that envisage a socio-economic system in which property and the distribution of wealth are subject to social control.  As an economic system, socialism is usually associated with state or collective ownership of the means of production. This control, according to socialists, may be either direct, exercised through popular collectives such as workers’ councils, or it may be indirect, exercised on behalf of the people by the state.
and Economic Progressivism includes
…things as support for a mixed economy and progressive taxes in order to compensate for the perceived disadvantage to increase their income and sources of revenue to the poor when compared to the wealthy, in order to fix issues with society which are perceived to violate social justice. Economic progressivism draws advocates from all segments of the moderate left-wing, including social democrats and some liberals.
Their opposition includes proponents of laissez-faire.
So, it seems that Progressives can believe in socialist things, such as a more controlled economy, but not necessarily. I would say that progressive taxation is not really a socialist measure, though I believe excessive taxation can limit the free market.
Also, business regulations may not necessarily be a socialist measure, but it depends on the extent, and the type of regulation. Concerning extent, the more laws that are passed regulating an industry, the more control the government has. However, I would not say anyone lobbying or legislating regulatory measures is a socialist; I think it is a spectrum, and being a complete laissez-faire capitalist may not even be a good thing (I am still working out those issues as to how far gov’t should be involved in regulating health and safety in industry). So when I say someone is not a true 100% capitalist, that’s not even a bad thing.
The type of regulation is a bit more abstract. I tried to cover this in a previous post,Foundations of a Free Market, but I don’t even know if I explained it that well. The idea is, it depends on why the regulation is in effect. Socialism typically refers to controlling the means of production, so regulations that attempt to do this, for the very reason of “controlling the means of production”, are typically more socialist. However, regulations that come about for other reasons, such as health and safety, are not necessarily socialist. For instance, labeling laws, or occupational safety laws, are not necessarily socialist, or at least not to a great extent. They do control businesses to some effect, but it is not done so to interfere with the distribution of goods, but done for reasons somewhat external to the production process, namely, the health and safety of the customers and workers. In other words, if one was taking a quiz that placed someone as 100 (pure capitalist) and 0, pure socialist, health and safety regulations would score a -1, whereas laws that control production would be a -10.
In the Foundations of a Free Market post, I listed four main things, which are by no means exhaustive, that separate a Free Market from a Socialist Economy.
1) The right of people to sell a product for whatever price they want. i.e. no gas price caps
2) The right of people to negotiate wages. – i.e. no gov’t caps on CEO pay, at the complete capitalist end, this would mean abolition of the minimum wage.
3) Freedom in choosing what products to sell (not counting moral legislation, which is more of a social issue, not economic). – i.e. an insurance company being able to sell coverage they choose, not in packages determined by a state government, a restaurant owner opening a smoking restaurant (although this is more of a property rights issue), and iTunes selling music in any format they wish.
4) People having the freedom to start their own business – i.e. city governments not making decisions on what or how many businesses are allowed in their towns. For instance, a local government should not be able to say, “we already have enough taxi businesses, you cannot start your own”, or someone starting a business should not have to do a presentation demonstrating why their business should be profitable to a city council.
People may not agree to all of these, or not to a full extent. Again, incomplete agreement does not make someone a Socialist, again, it is really a spectrum. Most people are not either-or. Most Americans support the minimum wage, that just means they aren’t complete laissez-faire capitalists, and whether that is a good or bad thing is not even the point. I am nowhere near an expert on what makes a true capitalist economy, and am by no means the standard-bearer for this issue; I just realize there is some confusion at times on what makes someone a socialist vs. just being a Progressive (i.e. American Democrat). While Democrats are more likely to support socialist ideas, they hardly have a monopoly on them; many of the loudest voices concerning the gas price caps have been Republicans.
The main point is this: socialism primarily tends to mess directly with the means of production, typically through controls of wages and prices, or through determining who can sell what. Other measures may produce less economic freedom, but socialism messes with the market directly.