democracy
dĭ-mŏk′rə-sē
noun

Government by the people, exercised either directly or through elected representatives.A political or social unit that has such a government.The common people, considered as the primary source of political power.

The American Heritage® Dictionary of the English Language, 5th Edition.

From Greek Demos: people + -ocracy: rule. Rule by the people

re·pub·lic (rĭ-pŭb′lĭk)
n.

1. a. A political order whose head of state is not a monarch and in modern times is usually a president.
   b. A nation that has such a political order.

2. a. A political order in which the supreme power lies in a body of citizens who are entitled to vote for officers and representatives responsible to them.
   b. A nation that has such a political order.

3. often Republic A specific republican government of a nation: the Fourth Republic of France.
4. An autonomous or partially autonomous political and territorial unit belonging to a sovereign federation.
5. A group of people working as equals in the same sphere or field: the republic of letters.
   [French république, from Old French, from Latin rēspūblica : rēs, thing; see rē- in Indo-European roots + pūblica, feminine of pūblicus, of the people; see public.]
   American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

They are certainly not the same thing.

From a 1935 edition of a Thorndike dictionary (I like to refer to older dictionaries for more precise definitions or to compare how words have been politically or socially changed in their usage over time.) Republic just means: "a nation or state where the citizens elect their rulers".

Anyway, the US is not a universal democracy but a limited democracy and is a republic. Democracy to me is just a collective means of decision-making.

The USSR claimed to be democratic. It was the Union of Soviet Socialist Republics. A citizen could vote for a representative from his district so it was democratic in that sense but the people didn't rule, the State did. The representative was more representive of the State than the people. The Democracy was more or less a farce. As is the Democratic People's Republic of North Korea (DPRNK)
People voting for their rulers is a republic. Representatives voted to represent the people who will rule over them is democratic but the democracy is becoming more of a farce.

when in doubt, always ALWAYS say to them ~ recite the Pledge of Allegiance ~ to the Republic

then you will find that they are the globalist indoctrinated leftist ideologue embracing socialist democratic marxism that they usually cannot explain coherently or rationally without becoming upset with denial symptoms and making accusations/distractions, and when they do crack, then you know you have got them. You have broken down the barrier of the psychological moment of their inception.