A reoccurring meme posted by conservatives and constitutionalist types will look something like this:
“In a democracy, as long as a majority decides they want something, they can take it from you. But in a republic, you have inherent rights to your property that cannot be taken away. America is a Republic, not a democracy.” It exists in various incarnations as image macros (text over a picture or background) and as an argument in comments sections expressed with varying degrees of coherency, usually to bitch about how liberals are greedy asshole thieves.
It exists as an effort to explain the concept of what President John Adams called the tyranny of the majority, a fundamental point of debate in political theory. What it actually is is being pedantic, and completely wrong at that. As a pedantic asshole, I’m all for pedantry. But FFS, you gotta understand what you’re yelling about before you be a dick to people.
So what is the actual, functional difference between a democracy and a republic? Etymology. That’s it.
“Republic” comes from Latin, whereas “Democracy” comes from Greek. Republic comes from the expression res publica, which means “the public thing”. It is one of the very few instances where the “re” isn’t a prefix meaning “again”. Res is actually preserved in its ablative form as re, used when sending messages in regard to a pre-established subject, i.e. “re: [subject]”. It is not short for “regarding”, although that works as a mnemonic. Res is a fairly vague term, meaning something in the ballpark of thing, matter, concern. The republic, then, is a matter of public concern. It was used to refer to the representative democracy put in place after the end of the Roman monarchy, which is traditionally put at 509 BC (the historical precision of this date is dubious, but nonetheless not completely implausible). Interestingly, calling a representative government “thing” is not limited to the Romans. Old Norse and Old English (which shared a common linguistic root) used the word þing (thing) to describe their assemblies of representatives as well. I’m not sure if it is a calque, or an independent development. The world’s oldest extant parliament is Iceland’s Althing, founded in 930 AD.
Democracy is from the Greek demokratia, from the roots demos, meaning “people”, and kratos, meaning “power”. It exists as an antonym to aristokratia, which is rule by an elite. Aristos literally means “excellent”, and it had a political connotation that varied in context. Technically, it does not mean “rule” by the people, which would be demarchy, but this is a mere etymological factoid. Aristocracy and democracy were grandfathered in by the ancients before political science slapped -archy at the end of every term. Nonetheless, it does not carry an implicit negative connotation of “mob rule”. That has been invoked since ancient times, yes, but it is not a meaning inherent in the term. The Greco-Roman historian Polybius–who’s work actually helped contribute to the ideas enshrined in the US Constitution–gave us a fancy term for that: ochlocracy.
From a political science standpoint, they’re interchangeable terms. In political science, there is a distinction between representative democracy and direct democracy, and a representative democracy can also be called a republic (or republican, adjectivally). So using poli-sci terms, all republics are democracies, but not all democracies are republics. But unless you’re speaking with this distinction in context, pedantry is unwarranted. A representative democracy is a system of government where enfranchised voters choose representatives to control functions of the government, while a direct democracy has enfranchised voters directly decide matters by vote. And these systems are not mutually exclusive. Smaller local governments using democratic systems tend to incorporate direct democracies. Many States in the USA have direct democratic options, usually referenced as a trinomial: initiative, referendum, and recall. Switzerland has been dedicated to using referenda at the national level since 1798. Both the US and Switzerland, though, have most of their governmental decisions effected by elected representatives, both at the national and state levels (states are called cantons in Switzerland).
The regulations of how a direct or representative democracy functions are based off of a constitution. There are no inherent rules defining a constitution. Any document that regulates how a governing body can govern is a constitution. Constitutions can enumerate protections of rights, but they also lay the framework for how rights are mutable in certain circumstances, which is the whole point of a government. Normally, you have the right to keep your money. Taxes are an instance where this right is superseded by government. A constitution can regulate the means and amount of taxation. It could say that an referendum of voters that exceeds 50% of a vote is sufficient to allow any tax proposal. Or it could require that elected representatives pass a bill with 2/3rds concurrence. The type of democracy has no bearing on the fact that rights can, in certain prescribed circumstances, be superseded.
The debate about what rights are, and to what extent they ought to be guaranteed is pretty much the entirety of debate in political theory. It’s not a new concept, and it certainly hasn’t been settled by the advent of American republicanism. Both the Greek democratic states and the Roman Republic, as well as the representative governments that followed them had to address the issue of majority groups oppressing minorities. They dealt with this by restricting political power. Universal suffrage by adults is a very new concept historically. The French were the first to grant it to all adult men, in 1792. The US, despite its reputation as being the major catalyst in crystallizing representative democracy as the government system of choice in the modern era, actually didn’t have universal male suffrage, even for whites, until the passage of the Fifteenth Amendment in 1870–although by then universal suffrage for white males was effectively the norm by then. In the days of Greece and Rome, actual legal class distinctions determined political rights. As time progressed, this softened into property ownership as the primary justifier of political power. The reasoning goes that people with the most to protect and the most to lose–as far as assets go–would have the most interest in making informed policy decisions. It’s obviously not bulletproof reasoning, but there is a rationality in giving people with property to be taken more say in if or how it can be taken.