"…promoting equality (as valued by socialism) will inherently require restrictions on liberty (as valued by libertarianism), forcing the society to choose one or the other as their primary value."
I’ll 2nd Thomas.
Joseph Dejacque first used the term to call Pierre-Joseph Proudhon’s defense of sexism "libéral et non LIBERTAIRE." For Dejacque, it seems, an anarchism which condemned the state, and some other hierarchies, was merely [radical classical] liberal, while an anarchism which opposed every hierarchy was libertarian. (in this sense, anarchism and libertarianism have more than traded meanings).
http://joseph.dejacque.free.fr/ecrits/lettreapjp.htm
There were other notable differences; Dejaque was a communist anarchist, and Proudhon was a market anarchist, but both were considered anarchists and socialists.
Later in the 19th century, the socialist movement split between the state socialism of Marx et al. and the libertarian socialism of Bakunin et al., sometimes called anarchism and sometimes called libertarianism.
In the 20th century, however, state socialists have often redefined socialism to exclude anarchism, while anti-state capitalists have also redefined libertarianism and anarchism to refer to limited-state and no-state versions of their theories. So both "socialism" and "libertarianism" need another word to explain *which* socialism or *which* libertarianism they refer to.
Libertarian socialism is libertarian in the same senses that libertarian capitalists use, e.g. the non-aggression principle. Malatesta wrote that:
"In the anarchist milieu, communism, individualism, collectivism, mutualism and all the intermediate and eclectic programmes are simply the ways considered best for achieving freedom and solidarity in economic life; the ways believed to correspond more closely with justice and freedom for the distribution of the means of production and the products of labour among men. … But in the long run it is always the searching for a more secure guarantee of freedom which is the common factor among anarchists, and which divides them into different schools."
http://dwardmac.pitzer.edu/Anarchist_Archives/malatesta/note.html
However, libertarian socialism is not always socialist in the various senses which libertarian capitalists use, and vice-versa.
Anarchist, Marxist, and pro-capitalist definitions of socialism have steadily diverged since the mid 19th century.
Ben Tucker wrote this definition:
"Socialism is the belief that the next important step in progress is a change in man’s environment of an economic character that shall include the abolition of every privilege whereby the holder of wealth acquires an anti-social power to compel tribute."
http://fair-use.org/benjamin-tucker/instead-of-a-book/armies-that-overlap
And many modern anarchists use similar definitions:
"The various schools of socialism present different solutions to this exploitation and subjection. From the nationalisation of capitalist property by the state socialists, to the socialisation of property by the libertarian communists, to the co-operatives of mutualism, to the free market of the individualist anarchists, all are seeking, in one way or the other, to ensure the end of the domination and exploitation of labour by capital. The disagreements between them all rest in whether their solutions achieve this aim and whether they will make life worth living and enjoyable (which also explains why individualist and social anarchists disagree so much!). For anarchists, state socialism is little more than state capitalism, with a state monopoly replacing capitalist monopolies and workers being exploited by one boss (the state) rather than many."
http://www.geocities.com/CapitolHill/1931/secG1.html
The pro-capitalist writer Mises, having defined "socialism" in terms of state interventions, found that most socialists understood socialism in quite different terms (and defined "syndicalism" very widely to include all these):
"In the minds of the great bulk of workers who call themselves socialists or communists, Syndicalism presents itself, at least as vividly as Socialism."
http://www.mises.org/books/socialism/part2_ch16.aspx
The various libertarian capitalists often borrow Mises’ definition, which, by his own admission, doesn’t match socialist definitions of socialism. Hence the confusion.