http://www.webpages.uidaho.edu/engl_258/lecture%20notes/capitalism%20etc%20defined.htm
Defining Capitalism, Communism, Fascism, Socialism
Caveat: There are some inherent pitfalls trying to offer simple, bite sized definitions of capitalism, socialism, communism and fascism – the first being that these are complex concepts concerning both economics and government, so short definitions will be incomplete; the second being that these concepts are not always mutually exclusive (most modern states combine elements of more than one); the third being that historical states defined the terms differently; and finally, some of the terms refer strictly to economic systems (capitalism) while others (fascism) also refer to government and economic systems (communism and fascism).
For a point of reference, the United States is a Constitutional Democratic Republic that has long embraced both capitalism (free markets) and socialism (public schools and universities, and public works – parks, roads and highways, sewer and water, dams, harbors, as well as social welfare, such as worker’s comp, unemployment insurance, social security etc.).
Capitalism
In common usage, the word capitalism means an economic system in which all or most of the means of production are privately owned and operated, and the investment of capital and the production, distribution and prices of commodities (goods and services) are determined mainly in a free market, rather than by the state. In capitalism, the means of production are generally operated for profit.
In a purely capitalist economy, there would be no public schools, no state owned or maintained roads and highways, public works, welfare, unemployment insurance, workers compensation, Social Security benefits etc.
Socialism
Most generally, socialism refers to state ownership of common property, or state ownership of the means of production. A purely socialist state would be one in which the state owns and operates the means of production. However, nearly all modern capitalist countries combine socialism and capitalism.
The University of Idaho, and any other public school or university, is a “socialist” institutions, and those who attend it or work for it are partaking in socialism, because it is owned and operated by the state of Idaho. The same is true of federal and state highways, federal and state parks, harbors etc.
Communism
Most generally, communism refers to community ownership of property, with the end goal being complete social equality via economic equality. Communism is generally seen by communist countries as an idealized utopian economic and social state that the country as a whole is working toward; that is to say that pure communism is the ideal that the People’s Republic of China is (was?) working toward. Such an ideal often justifies means (such as authoritarianism or totalitariansim) that are not themselves communist ideals.
Fundamentally, communism argues that all labor belongs to the individual laborer; no man can own another man's body, and therefore each man owns his own labor. In this model all "profit" actually belongs in part to the laborer, not, or not just, those who control the means of production, such as the business or factory owner. Profit that is not shared with the laborer, therefore, is considered inherently exploitive.
Fascism
The word descends from the Latin ‘fasces’, the bundle of sticks used by the Romans to symbolize their empire. This should clue you in that Fascism attempts to recapture both the glory and social organization of Rome.
Most generally, “a governmental system led by a dictator having complete power, forcibly suppressing opposition and criticism, regimenting all industry, commerce, etc., and emphasizing an aggressive nationalism and often racism.”
Unlike communism, fascism is opposed to state ownership of capital and economic equality is not a principle or goal. During the 1930s and WWII, communism and fascism represented the extreme left and right, respectively, in European politics. Hitler justified both Nazi anti-Semitism and dictatorship largely on the basis of his working to fight-off communism.
The church also played a major role in all of the European fascist countries (Germany, Italy, Spain, Portugal) as the authority on religious and moral issues, which was opposed to the threat of "godless communists".
Mussolini, the Italian father of Fascism, writes that: “..Fascism [is] the complete opposite of…Marxian Socialism, the materialist conception of history of human civilization can be explained simply through the conflict of interests among the various social groups and by the change and development in the means and instruments of production.... Fascism, now and always, believes in holiness and in heroism; that is to say, in actions influenced by no economic motive, direct or indirect. And if the economic conception of history be denied, according to which theory men are no more than puppets, carried to and fro by the waves of chance, while the real directing forces are quite out of their control, it follows that the existence of an unchangeable and unchanging class-war is also denied - the natural progeny of the economic conception of history. And above all Fascism denies that class-war can be the preponderant force in the transformation of society....
After Socialism, Fascism combats the whole complex system of democratic ideology, and repudiates it, whether in its theoretical premises or in its practical application. Fascism denies that the majority, by the simple fact that it is a majority, can direct human society; it denies that numbers alone can govern by means of a periodical consultation, and it affirms the immutable, beneficial, and fruitful inequality of mankind, which can never be permanently leveled through the mere operation of a mechanical process such as universal suffrage....”
A Note On Morality: Capitalism and socialism are essentially a-moral* terms: they simply refer to economic systems – who owns what and how capital is exchanged – regardless of any other type of moral principle or goal. Communism and fascism, on the other hand, refer to both economics, governance, and basic moral principles: that is to say they refer to overarching ideas about how people should live (rather than describing how people do business), so they imply a total ideology: a morality, an economy, a government.
* A-moral simply means neither moral or immoral. A rock is a-moral. Driving a car is usually a-moral. Killing someone with a rock is usually immoral. Driving drunk is immoral.