George Orwell defines "socialism"

In early 1941, George Orwell finished a long essay (it spans fifty-eight pages in my anthology) called "The Lion and the Unicorn: Socialism and the English Genius."

In it, Orwell touches more explicitly on ideological topics than is his tendency. He argues in favor of nationalism broadly speaking. Nations, in his telling, are based on real cultural difference and measured nationalism – patriotism and pride in one's country – is perfectly natural and good on balance. That's one of few points at which his analysis proves less than oracular. The collapse and division of the British Empire, among others, would expose the borders of nations in most of the world as arbitrary in a way that perhaps they are not in Western and Central Europe.

His definitions of socialism and fascism, though, are worth reading in full.

However, it has become clear in the last few years that 'common ownership of the means of production' is not in itself a sufficient definition of Socialism. One must also add the following: approximate equality of incomes (it need be no more than approximate), political democracy, and abolition of all hereditary privilege, especially in education [...] Centralized ownership has very little meaning unless the mass of the people are living roughly upon an equal level, and have some kind of control over the government. 'The State' may come to mean no more than a self-elected political party, and oligarchy and privilege can return, based on power rather than on money.

... and fascism ... 

Fascism, at any rate the German version, is a form of capitalism that borrows from Socialism just such features as will make it efficient for war purposes [...] But the idea underlying Fascism is irreconcilably different from that which underlies Socialism. Socialism aims, ultimately at a world-state of free and equal human beings. It takes the equality of human rights for granted. Nazism assumes just the opposite. The driving force behind the Nazi movement is the belief in human inequality , the superiority of Germans to all other races, the right of Germany to rule the world. Outside the German Reich it does not recognize any obligations.

To Orwell, the most important difference between the two systems is that the goal of the former is to eliminate social inequality and that of the latter is to calcify caste based on notions of racial biology rather than on class or wealth. He makes the argument in an attempt to explain the overwhelming sympathy (if not outright support) of the wealthy for fascism until 1939 even as it ran counter to the national interest. Orwell's conclusion is that, so long as status insulates a wealthy person from the adverse effects of a revolution, he will support that which preserves his social position.