Phil, you describe a 'DecentralizedLeft' as:
"A left wing which doesn't believe in putting all it's faith in the NationState, but it social solutions organized in the same way as it's protests methods, through a network of different grassroots organizations and institutions of different scales."
and ask: is this the same as Anarchy / Anarchism?
I would think the description you give is pretty much a classic characterisation of anarchism. Eg here is Kropotkin's famous definition from the 1910 Encyclopaedia Britannica:
"ANARCHISM, the name given to a principle or theory of life and conduct under which society is conceived without government - harmony in such a society being obtained, not by submission to law, or by obedience to any authority, but by free agreements concluded between the various groups, territorial and professional, freely constituted for the sake of production and consumption, as also for the satisfaction of the infinite variety of needs and aspirations of a civilized being."
He goes on to talk about an 'interwoven network' of groups, and "Moreover, such a society would represent nothing immutable. On the contrary - as is seen in organic life at large - harmony would (it is contended) result from an ever-changing adjustment and readjustment of equilibrium between the multitudes of forces and influences, and this adjustment would be the easier to obtain as none of the forces would enjoy a special protection from the state."
So there you have your EmergentDemocracy as well.
Of course, one big difference between anarchism and marxism is that there is no canon or theoretical authority to give definitions. Different people calling themselves anarchists have different accounts. Also, anarchism has always had a bad name - like many political labels it started out as a pejorative. So some people took on the label with gusto, but others who are often viewed as anarchist thinkers distanced themselves from the term. (Tolstoy is a particular example.)
Re discussions on the wiki about right/left and hierarchy and centralism. I think we need a quick look at the history of 'the left' on this.
To monstrously oversimplify:
Back in the 18th century there were all sorts of ideas- democratisms, utopianisms, reformisms, quasi-religious millenarianims etc about. The term left arose from seating arrangements in the French Legislative Assembly of 1791 (I think in an earlier parliament the left-wingers sat in the higher up seats and were called 'the mountain'.)
In the 19th century, as 'proletarianisation' gathered pace, according to many accounts you can identify two main streams of 'left' thinking (not to deny all the other varied strands). In the First International ('International Working Mens Association') the left split into two main groupings which you could label 'authoritarian' and 'libertarian', or 'statist' and 'anti-statist', with emerging figureheads in Marx and Bakunin. Thus was born 'Marxism' and 'Anarchism' as we know them.
These broad groupings contained all shades and factions, but I think it's fair to say that in the nineteenth century the 'authoritarian left' was more focussed around parliamentary activity than violent revolution. The split probably had a lot to do with geography and personal allegiances. If there is a clear ideological divide it is over the issue of whether workers movements should try to capture the nation state through parliamentarianism, or ignore the state and build up their own 'autonomous' organisations instead.
Who was in the right, and in the majority, is hotly disputed. What I think you can say - the idea of the left as a statist project was definitely not unanimous. Probably the majority of 'leftists' in France, Belgium, Switzerland, Spain, Italy were thinking along the lines of co-operatives, syndicalism, mutualism etc. with little or no interest in state centralism. By the start of the 20th century Syndicalism, eschewing any involvement with statist politics, was the major force on the left in France and Spain. There were also important syndicalist movements in Britain and the US.
All this changed with the Russian revolution. The Russian revolution seemed to be a living proof that taking over the NationState was the way to go. Within a few years of 1917 the whole character of 'the left' had completely changed. The main-streams were now revolutionary marxism and parliamentary reformism. The French syndicalist federation CGT became a wing of the communist party, syndicalists in Britain and US went over to the party. The only remaining anarchist-influenced mass movement was in Spain.
The best part of a century later I think Russia stands as a living proof that taking over the NationState wasn't the way to go. This doesn't of course prove that there was more to be said for libertarian socialist projects. What I'm saying is that if we want to start talking about a decentralised left then, like it or not, we are not starting from nowhere.
Terminology - Most people say Proudhon was the first to openly accept the term anarchist, previously used as an insult by political opponents. I think 'Libertarian' was taken up by other anarchists less comfortable with the black cape, round bomb image associated with the a-word. I couldn't say exactly when, but in 1926 the Dolos Truda group of Russian anarchist exiles wrote 'The Organisational Platform of Libertarian Communists' and in 1932 Isaac Puente wrote the Spanish CNT programme 'Comunismo Libertario'. According to what I read on Wikipedia the right-wing Libertarian Party was founded in 1972 and 'The term 'libertarianism' in this sense (although in itself much older), has only been largely used since 1955'.
See also :
Anarchist Studies Journal : http://www.l-w-bks.co.uk/journals/anarchiststudies/contents.html
WikiPedia on Libertarian Socialism : http://en.wikipedia.org/wiki/Libertarian_socialism
Anarchopedia : http://eng.anarchopedia.org/Main_Page
BertrandRussel on anarchy, socialism and syndicalism : http://onlinebooks.library.upenn.edu/webbin/gutbook/lookup?num=690