Great article, that concludes the topic for me and I won't have to write anything about it any more :) thanks for writing it out so well!

Let me dive a bit into the political stuff about the socialism/communism definition, because you started and it's kind of a hobby of mine :D
First off, there are countless socialist schools. Their former main organ, the international, split up several times because everyone thinks he is right and the others are counterrevolutionaries.

According to Marxists, socialism is the phase of the so called "dictatorship of the proletariat". Communism means that socialism has advanced so much that the state disappears. Wikipedia
This is why communists today say that there has never been real communism, and by pure theoretical definitions they are right. They fail to see that every attempt to get there in the ways Marx described led to terror and suffering.

Libertarian socialism has lots of different branches itself and actually is a synonym for anarchism (except in the view of ancaps, a bit more on them later).
It all started with Proudhon's Mutualism (Property is theft. Property is freedom). Around the same time American small business owners developed a concept of left-market anarchism in opposition to the growing corporations which used the state to suppress their competition. That stayed a mostly American phenomenon though, in Europe the thinkers started to play with ideas which would base on abolition of wage labour and markets together with the state, mostly in favour of a distribution of goods not involving currency.
Based on Proudhon, Bakunin formulated anarcho-collectivism and Kropotkin anarcho-communism. The main difference between the two is that in collectivism people would get their share of goods depending on the work they submitted, thus involving some kind of currency at least in the beginning, while communism means that it's distributed completely freely according to needs (same as Marx:
"from each according to his ability, to each according to his needs").
Both had big issues with Marx and basically foresaw that his ideas of a socialist dictatorship will lead to power structures which won't just disappear, but do everything necessary to stay in power and suppress everyone else.
Later in history, anarcho-syndicalism became very popular, which is the idea that trade unions and collectives can overthrow the state and capitalism, again building on the previous thinkers. Around the 1920s/1930s they were very successful in certain regions for a while (Ukraine, Spain before/during the Civil War - Orwell fought on their side and wrote the autobiographic Homage to Catalonia about his experiences), but in the end always brutally suppressed by Leninists/Stalinists, Capitalists and Fascists, often working together.
Their organizations still exist, but are very small in numbers. A famous proponent of their ideas today is Noah Chomsky.

There are countless further categories which can be taken more or less serious (A-feminism, green A, Christian A, A-pacifism, Egoist A, Primitive A, Insurrectionary A, Post-left A, Transhumanist A), as well as the "non-anarchisms" which also want to abolish the state, but keep certain power structures intact or even extend them and are not based on voluntarism, like National-A (National Autonomous Zones, natural hierarchies), A-fascism (similar to the previous, but less thought out and basically just a rant by a racist and misogynist kid against the Swedish state) and A-capitalism (money rules, greed is good).

Most info collected from Rationalwiki, because I'm really bad with remembering names and stuff and didn't want to leave anything out. It's generally a great site if you're interested in political theories, philosophies, religions and more.