You're right, but you're also wrong too. It's a condition I often find myself in. :)
Socialism, communism, and capitalism are examples of economic systems. With socialism, the state owns everything and doles it out to "each according to his need", or so the brochures claim (incidentally, this is why people often confuse socialism with a governmental form, because the state is so central to that system). In communism, everyone owns everything and everything is supposedly shared equally (ironically, every nation we think of as 'communist' isn't even close to being that). In capitalism, individuals own what they own, and distribute it (or not) according to their own will, and the market basically runs itself and is a bit more... organic.
Dictatorship, democracy, republic, and theocracy are governmental systems. They're not absolute either, meaning you can have hybrids. In dictatorship, one person (or body of people, aka 'republic') rules/owns/manages everything, usually including the people themselves. A democracy is rule by majority referendum, and will almost always evolve into it's own 'special' version of a dictatorship. A republic is a government comprised of a body of representatives, which can be selected any number of ways (In pre-Julian Rome, the Senate was essentially hereditary, though not officially). A theocracy is basically 'church=state', and can have elements of any of the others.
Nazi Germany was a pure dictatorship. South America is a great place to find examples too (when one candidate gets 98% of the "vote", chances are your "election" was a sham). The Soviet Union was also a dictatorship, but there were elements of a republic present (honestly, I'm not up on the relationship between the Premier and the rest of that government). England started out as a dictatorship, but evolved into more of a republic (the English Monarch is more of a novelty than a ruler at this point). The US started out as a democratically-elected republic, but it has taken on more and more elements of a direct democracy over time. The Middle East is lousy with Theocracies. Post-Constantine Rome, while remaining a dictatorship with republican elements also evolved into a kind of Theocracy.
Marxism was just one man's take on republic government and socialist economy (looks great in theory). Just as James Madison had his take on a democratically elected republic government with a capitalist economy.