A classical democracy is Athenian or in the American sense, ye olde New England Town Meeting where everyone has a vote (depending on qualifications, like being property owners, etc)
at some point it doesn't scale well, and you have to use representation with a written organizational structure (a constitution)
Note the Republic of Venice. Venice followed a mixed government model, combining monarchy in the doge, aristocracy in the senate, and a "democracy" of Rialto families in the major council. This is not exactly the American model of republic.
On the other hand, many offices in the Athenian democracy were filled by lottery .
Yet in casual conversation, representative democracies of various types are often refereed to as simply "democracies"
No. That's not necessarily wrong but that's not how it goes.
Or maybe I should say that's simpler than all that. At least where we care.
A democracy rules by will of the people. That is to say that on anything, the people are given a vote. This is "rule of the people." For example, a man is a suspect in a rape. There does not need to be a trial, only a vote of those present if he is guilty. No evidence, no trial. He might get a trial but it's not guaranteed. At any time, the will of the people may change and decide that the new sheriff only needs two accusers instead of evidence.
A republic is a governing system whereby people vote on the laws that dictate what happens. The same man is now guaranteed a formal trial, investigation, by other people and has protection such as no torture or punishment until he is found guilty. If the people are not happy, they petition to change the law and then vote on the proposed changes. This is "the rule of law."
A Constitutional republic is a government where those laws and rules are written down and followed. It's the government's promise as to what it will and will not do. Rights are usually enshrined in or with the Constitution and require a significant percentage of the people to vote for changes.
These are very large and distinct differences and it is always important to make sure that everyone you engage knows the difference.
you might find these interesting/novel
https://en.wikipedia.org/wiki/Constitution_of_the_United_Kingdom
https://en.wikipedia.org/wiki/Roman_Constitution
https://en.wikipedia.org/wiki/Constitution_of_the_Athenians_(Aristotle)
etc
Just to be sure, you know the difference between a democracy and a constitutional republic, right?