Well, that's just socialism, not communism--I would guess you would accept
the same source's definition of communism as your definition of communism, but I don't want to assume on that point.
But, focusing on socialism, the definition offered by your link is:
1: any of various egalitarian economic and political theories or movements advocating collective or governmental ownership and administration of the means of production and distribution of goods
2:
a: a system of society or of group living in which there is no private property
b: a system or condition of society in which the means of production are owned and controlled by the state
3: a stage of society in Marxist theory that is transitional between capitalism and communism (see communism sense 2c) and is distinguished by unequal distribution of goods and pay according to work done
Now, the original claim you made was that "Democrats don't want socialism and communism any more than true conservatives want oligarchy and fascism." Therefore, for the other posters who took issue with this claim, you should do one the following:
1) Demonstrate Democrats want something that falls under these definitions of socialism
OR
2) Explain why the above definitions should be considered incorrect, then offer what you think is the correct definition, and show that Democrats want that
Doing so would likely lead to a more productive discussion on the topic, by ensuring all are on the same page in regards to the definitions.