socialism-The belief that all property should be held by the state or in common. Since most libertarian socialists are anarchists they believe in property being held in common, meaning anyone can use what ever they want whenever they feel like it.
Basically, while libertarian capitalists believe all force and coercion is wrong unless used to defend one's person or property libertarian socialists believe all force and coercion is wrong unless used to defend one's person, but not one's property since all property was originally founded on theft and relies on state coercion. Without state coercion capitalists would have to create private organizations (basically, miniature states) to enforce property 'rights'. Libertarian capitalists ignore the fact that companies would monopolize land and exclude certain companies, eventually leading to vast tracts of private property that function like modern states do.
see also: anarchism
A libertarian socialist would argue that a society based on such huge disparities of wealth is unfree. If you wish to enter into employment, you choose first and take orders later (as with liberal democracy). Libertarian socialists believe in voluntary association and economic democracy. This will allow the individual to reach his/her full potential.
The most famous example of successful libertarian socialism is the anarcho-syndicalist experiment in Spain during to Spanish Civil War, which was eventually destroyed by Communists and Fascists (see Orwell' "Homage to Catalonia" for excellent first hand reportage of this). At its peak, the anarchist union (CNT) had one million members.
Although sharing much of (if not all of) the Marxist analysis of capitalism, lib socialists vehemently oppose state socialism, especially the authoritarian socialism of Lenin, Trotsky, Mao and, more recently, the socialism of Hugo Chavez. The modern dispute between the two schools of socialism began in the First International, in which Karl Marx and Mikhail Bakunin bitterly argued over the road socialists should take. This dispute has continued ever since, with many Marxist regimes imprisoning, murdering (Russia), and exiling (Cuba) anarchists.
Socialism = the abolition of privately held means of production.
A libertarian socialist sees the state as a coercive authoritarian institution which the elite uses to exploit the people. A libertarian socialist sees capitalism as a way for the ones with money, i.e. power, to enforce oppression on the ones who don't.
Free market is about as fair as the freedom to kill an innocent person.
Libertarian - values personal freedom, private property, and minimal inference of the state. Citizens are independent and self reliant.
Socialism - No private property, property is owned collectively or by a centralized government that often plans and controls the economy.. Maximize the size of government and government intervention in the lives of its citizens. Citizens are dependant upon the State.
Government is the only organization specifically granted the power to use force to achieve its goals.