What is the difference between democratic and non-democratic elections?

Democracies hold democratic elections. Authoritarian governments hold non-democratic elections. A "real" election is only possible in a democracy. Non-democratic elections are often used to prop up a dictatorship by giving it a false sense of legitimacy. There are some governments that include both democratic and non-democratic features.
Real democracies include freedom of speech and freedom of the press. Citizens in democracies are free to criticize their country's leaders without fear of retribution. In non-democratic countries, critics are often imprisoned or even killed. And in democracies, newspapers must be able to report on current events freely without government censorship.
Real democracies hold free and competitive elections. Voters must have real choices and the candidates they choose must actually take office. Voters' ballots must be confidential.
A quick analysis of the world map at Freedom House shows where democratic elections take place. Most of Europe holds democratic elections; in the Arab world, only Tunisia does. The Philippines and Turkey hold elections, but they are not really democratic.
https://freedomhouse.org/report/freedom-world/freedom-world-2018

The difference between democratic and non-democratic is clear cut and it changes the way elections are held. In a true democracy, individual citizens have input on matters of policy and who is in power in their nation. Therefore, elections truly take their votes into account and use the input of the citizens when deciding on their executive leader. In the United States, elections are held and each person in the country gets a vote, which is recorded and informs the Electoral College how to vote, giving the citizens input.
In a non-democratic government, general elections for the populace are largely for show—they have little impact on the true outcome of who is put in charge. These are often propaganda measures for the ruling party. Other times, elections will be legitimate but will not be open to the general populace; only certain groups may vote, essentially giving the ruling power to certain people—perhaps a group of cabinet members or another similar unit.

In a democracy, elections take place to give a voice to the people. Every few years or so, in competitive elections, the voters get to choose their elected representatives. If in due course they become unsatisfied with the choices that they make, the voters can always change their minds come the next election, when they can vote to remove the representatives they originally elected. Under a genuine democracy, governments are essentially lent power by the people, who have the right to take that power away from them the next time they come to vote. At the heart of the democratic ideal is the principle that those who exercise power over us should be removed from office when they no longer enjoy our support.
Elections are a routine feature of political life in countries without democracy. In such countries, elections are there primarily as a propaganda exercise, to confer a sense of legitimacy on the ruling government. These elections are far from being free or fair and are marked by fraud and numerous voting irregularities. But ultimately what matters to the government in such cases is the outward appearance of democracy rather than its actual substance. Elections are a way for authoritarian governments to claim that they really do represent the will of the people. Moreover, it's always much harder for opponents to challenge a regime which appears to have such widespread support.
As well as rigging elections, governments in non-democratic countries have complete control over the flow of information to their citizens. As such, it becomes difficult for opponents to gauge the precise level of public support for the government as well as the general level of hostility towards it. This serves to further consolidate the government's power.