In order to answer this question, I will define a democratic government. A non-democratic government is one that does not meet all the criteria for being democratic.
There are three aspects to democracy. In order to be democratic, a government has to have all three of these attributes. They are as follows.
Popular sovereignty. In a democratic government, the people must be in charge. This means that the people have to be the ones who elect their leaders. They have to have real choices in their elections and their leaders have to, for the most part, do what they people want. A nondemocratic government might have no elections at all or it might have elections that are just for show because the people do not have any real choices.
Political equality. In a democracy, everyone has to have an equal say. A true democracy cannot exist if some groups of adults have the right to vote while others do not. A true democracy cannot exist if some people’s votes count for more than others.
Political freedom. In a democracy, people have to have rights. They need to have the right to free speech and freedom of religion. They need to have the right to protest against the government. They need to be free from having the government come in and search their homes without warning. A government that holds elections but that also curtails these freedoms is not a true democracy.
The difference between these forms of government, then, is that democracies have the three attributes mentioned above while non-democratic governments do not have all (or maybe do not have any) of them.
Democratic government shows the interest of the general public, while non democratic government has other ruling methods such as dictatorship, socialism etc. The democratic respects people's opinions while the non democratic doesn't.