Okay, maybe Lithuanian will explain better to an Estonian:

Once in the 19th century there was a rapid industrialization. Farmers and citizen guild-workers lost their economical value and had to turn into factory workers. At that time, there was massive unemployment, and factory owners were unregulated. Then a philosopher Karl Marx went in, and started to analyse. He concluded that, in history, it's always 'slaves vs landowners', then 'peasants vs seniors', and ultimately 'workers vs enterprise owners (bourgeoisie)'. He named this phenomenon 'class struggle', and hypothesised that, after workers will defeat bourgeoisie, then it would be possible to create a perfect egalitarian society with no exploitation, in which people have all the rights except the right to be rich. That was called 'Communism', a proposed ideal society.

His ideas attracted many followers, which were split into several political campus, for instance, Socialist democracy ('mild' socialism, rich people pay more taxes, etc.), Anarcho-Communism (no state, no regulations, lived only for a short period of time in Ukraine), and many more.

Then V. Lenin came in, and told there must be a 'peasants' revolution' that abolishes the existing state(s), kill all the enemies of that revolution, become a Socialist country (ie. State controls all the economy) and then slowly progress into Communism. His practices were furthermore refined by Stalin and were called 'Marxism-Leninism'. History of the USSR shows that the power of a Socialist state can be used to create a totalitarian prison.

So 'Communism' can mean either an egalitarian society or heading towards that direction, basically.