Connecticut doesn't have slaves because they are illegal to have slaves
It is important because in 1836, during the Texas Revolution, somewhere around 200 rebels including Davy Crockett and James Bowie held out against 1,800 Mexican Soldiers under the command of Santa Anna, the Mexican dictator at the time, for thirteen days.
All three are ways of approaching the economic system and how much the government should be involved in that system.
Capitalism involves private ownership of businesses with little to no government interference or regulation. Most countries do not run on laissez-faire capitalism in which there is no gov't regulation. However more run as a blend between capitalism and socialism.
In socialism, the government owns the means of production and sets pricing, wages, quotas, and production. Often managers are government appointed and the workers all receive an equal wage for their work. Cooperation is key to the success of socialism. This is also the step between an overthrow of capitalism to full communism.
In communism, the means of production are owned by the people and the gov't is no longer needed to regulate business and/or wages. It is a complete cooperative state where the workers work for the good of all.