How was democracy in ancient Rome different from in ancient Greece?

Romans used a representative democracy wherein they had a system similar to the US Congress. Selected people called senators voted on issues rather than the whole population. I assume for the Greeks you mean the system of direct democracy attributed with Athens. In that system, the entire population voted on issues.

Today, although "democracy" and "republic" are often used interchangeably, in ancient times they referred to distinct political systems. A democracy and a republic each had its own distinct institutional arrangements based on different ideas about what it meant for citizens to participate in the political process. Although the United States reflects the influence of both democracies and republics, these influences can at times be in tension with one another: While a democracy represents the principle of majority rule, a republic uses institutions to check and balance the power of majorities.

Democracy was invented by the ancient Athenians in the sixth century B. C. It comes from the ancient Greek word "demos" or people and "kratos," meaning rule. Democracy was a political community in which the people, or the collective body of active citizens, exercised political power. In contrast, the term "republic" is Roman in origin and has traditionally been dated back to 509 B. C. It comes from the Latin word "res," meaning thing or matter, and "publica," meaning public or common. The republic, therefore, meant the public matter, the thing that is in common among the people.

Democracy was invented by the ancient Athenians in the sixth century B. C. It comes from the ancient Greek word "demos" or people and "kratos," meaning rule. Democracy was a political community in which the people, or the collective body of active citizens, exercised political power. In contrast, the term "republic" is Roman in origin and has traditionally been dated back to 509 B. C. It comes from the Latin word "res," meaning thing or matter, and "publica," meaning public or common. The republic, therefore, meant the public matter, the thing that is in common among the people.