Jonn Elledge had a nice piece in the New Statesman about free trade. The question he poses is how Brexiteers can exalt free trade but want to leave the most developed free trade area in the world, the EU. The answer he gives is to distinguish between ‘free to’ and ‘free from’. When economists talk about free trade they mean free to trade, which is what the EU has achieved through regulatory harmonisation in particular. Brexiteers mean ‘free from’ in the sense of trade free from government intervention.
I think we can go beyond what Elledge says and make exactly the same point about the term ‘free market’. A Brexiteer might think of a free market as a market free from government interference, including government regulations. An economist would be more likely to talk about a free market as one where people were free to trade in a socially optimal way. The state might be required to make that happen in many ways.
To take just one example, markets can sometimes not exist because of information asymmetries, but if those asymmetries are removed then people can beneficially trade. (Economists will immediately recognise this as Akerlof’s famous market for lemons.) Removing those asymmetries does not necessarily require government, but government could play that role. If it did, we would have a free market as an economist would define it, but only as a result of what some on the right might call government ‘interference’. As Mariana Mazzucato would argue, the state can also create markets through organising research and development.
Two governments that harmonise each others regulations can create better markets in both countries by increasing competition. Equally there are other government measures that make markets work better. The most obvious example is to reduce monopoly power, which reduces prices and increases the quantity traded in that market. In truth the idea of a market completely free from government is semi-mythical: all markets work within a legal framework created and enforced by the state. When some people complain about government interference in markets, and eulogise ‘free markets’, they are really just complaining about forms of interference they do not like and are using the notion of freedom to glorify their distaste.
Nevertheless, I think this distinction between ‘free to’ and ‘free from’ its perhaps a way of resolving something of a paradox that I talked about in my neoliberal overreach piece. The paradox was whether Brexit can be described as neoliberal, as it involves the apparent illiberal destruction of a free trade area. If you see neoliberalism in practice or ‘in action’ as not so much a coherent (if flawed) unified theory (as here, for example), but rather a collection of views that encompass not just free trade but also promotion of the market and dislike of certain market interference, then neoliberal overreach can occur in any of those dimensions. 
So those like Osborne who wanted a smaller state so taxes could be lower (and perhaps for other reasons to) went for austerity as a means of achieving that. Those, like most Brexiteers, who wanted less regulation (including no state interference in how they personally avoid paying tax) pushed Brexit, even though it involved reducing the ability to trade. What Colin Crouch calls corporate neoliberals turned a blind eye to growing monopoly and rent extraction.
While all three groups were happy to eulogise free trade and free markets, conflicts arise over the interpretation of free. For the Brexteers free trade means freedom from government interference, while for Osborne it meant free to trade. For corporate neoliberals free markets means markets that are free from government limits on monopoly and attempts to avoid rent seeking, while ordoliberals want the state to control monopoly so markets are free to work for society.
Today for most people most of the time the idea of freedom generates positive emotions (although that itself is a social phenomenon, as Adam Curtis among others explored.) It is therefore a word worth expropriating for a political cause if you can. But by noting that conflicts arise between ‘free to’ and ‘free from’ we can perhaps see that all politicians are doing is trying to promote a form of freedom that suits their cause.
 In an interesting piece, Will Davies argues against the need to want to define political or social terms precisely as if they “connect cleanly and unambiguously to some object”.