Question

how does a communist system of government differ from a democracy?

In a communist system, power is inherited and passed down. In a democracy, power is in the hands of the people.
In a communist system, elections are never held. In a democracy, the people vote in elections to choose their leaders.
In a communist system, voters choose from a wide variety of candidates. In a democracy, choice is somewhat limited.
In a communist system, a single political party controls the government. In a democracy, the people can elect officials from different parties.

Answer 1

Short answer: The two concepts are different kinds of things. "Communism" is an economic and political ideology (and in practice, a form of one-party/state system in many countries). "Democracy" is a form of government based on popular rule, elections and political pluralism. In practice, most historical communist states have been one‑party, centralized and not competitive democracies. Below I correct the four statements you gave and highlight the main differences.

Corrections to your four statements
- "In a communist system, power is inherited and passed down." — False as a general rule. Inheritance of power is a feature of monarchies or dynastic regimes. Most communist parties do not formally base leadership on heredity, though some real-world examples (e.g., North Korea) developed dynastic succession.
- "In a communist system, elections are never held." — False. Many communist governments hold elections, but they are often non‑competitive (single‑party lists or only approved candidates). The presence of elections does not by itself make a system democratic — competitiveness, secrecy of the ballot, and real choice matter.
- "In a communist system, voters choose from a wide variety of candidates. In a democracy, choice is somewhat limited." — Backwards in general. Communist one‑party systems typically offer limited or no choice; democracies normally offer multiple parties and candidates. That said, democracies can still have practical limits on choice (electoral systems, incumbency, barriers to entry).
- "In a communist system, a single political party controls the government. In a democracy, the people can elect officials from different parties." — This is generally correct as a broad contrast. Communist states historically are usually single‑party (the communist party dominates); democracies feature multi‑party competition and legal opposition.

Key contrasts (typical real‑world features)
- Political pluralism: Democracy = multiple parties, free opposition. Communist state = one dominant party, limited organized opposition.
- Elections and competition: Democracy = free, fair, competitive elections. Communist state = either no competitive elections or tightly managed/controlled elections.
- Civil liberties and rule of law: Democracy = stronger protections for free speech, press, assembly, independent judiciary (varying by country). Communist regimes often restrict these to protect single‑party rule.
- Economic system: Communism (as practiced) = state ownership or heavy state control of major means of production, central planning. Democracies can have many economic models (market capitalism, social democracy, mixed economies).
- Decision‑making and accountability: Democracy = separation of powers, periodic electoral accountability. Communist states = party/state fusion, decisions taken within the party hierarchy.
- Examples: Communist/one‑party states — Soviet Union (historical), People's Republic of China, Cuba, Vietnam. Democracies — United States, India, Germany, Sweden (these vary in political systems and economic policies).

Short summary
Communism (as implemented in most 20th/21st‑century states) tends toward one‑party, centralized political control and state economic ownership; democracy emphasizes political competition, pluralism and free elections. There is overlap and nuance in practice: not all democracies are identical, and not all countries that call themselves communist follow the same forms.