What's the difference, is the real question. It really depends upon what government was displaced by the military.
In any nation, the military will represent the establishment. It's just the nature of things. This means any time the military command thinks an intervention is needed, it's because the establishment is threatened. In the history of the 20th century, I can't recall a military coup which led to immediate democratic elections. It's more common to see democratic elections overturned by a coup.
So what does that have to do with the price of eggs in China?
The reason a military coup is so common is because the military has the needed organization and materials in place at all times. The key word is organization, because this means they can quickly restore and maintain order. It takes massive numbers of people in the streets to resist a military coup. Even then, a lot of people will be hurt in the process. At some point, even the most hardened General will give up.
Short of that, most people in the world have a short list of desires and any government which can provide them will have some support.
The immediate problem of living under a military government is it means everyone is subject to military policy and military justice. Military authority can be arbitrary and capricious. An officer is given an assignment and resources to accomplish his goal. If he produces the desired results, it's not likely his methods will be questioned.
In the military, cooperation is not optional. When this principle is extended to the civilian population, it eliminates most of the civil rights we expect from an enlightened government. There is no more presumption of innocence, no more burden of proof. The individual's rights are subordinate to the interests of the government, or whoever has power in the immediate area.
I remember a Sunday political discussion TV show from many years ago. One of the panelists was a newly retired Army General. The topic was some middle European country where people were very irritable and killing each other. The host turned to the General and asked, "What can the military do in this situation?"
The General didn't hesitate. He said, "We can destroy things and kill people."
"How would that help the situation?" the host asked.
"I don't think it would," the General replied, but unless you need stuff destroyed and people killed, don't call the military. That's the only things we do really well."
This points out the main problem with a military government. As an organization, an army is not meant to be a government. When someone tries to shoehorn an army into a government, it's not a very good fit.
The problem with a military coup is that it is non-democratic and the will of the populace plays almost no role in it.
All dictatorship's are essentially military-controlled societies, and all military controlled societies are dictatorships. Whether they got that way via a military coup or not is largely superfluous to the consequences once they become that way.
Just a dictatorship
can sometimes happen to be better
in the short-term for the populace (
with a wise benevolent dictator) than a democracy, a military coup can also accomplish things that benefit the populace and that a democratic government would not.
However, note all the bolded qualifications on that statement. Those make such a benefit unlikely, rare, and short-lived. The more common and near-certain long-term effect is very negative, because members of such government have zero motive beyond altruistic ethics to give any consideration to the public desires or welfare, and there are infinitely greater ways that those in power can benefit themselves by harming the populace than by helping them. So, odds greatly favor harmful policies by any form of dictatorship and thus military coup.
Also, once established, authority by force will never revert to a democracy unless by counter-force.
This is why those who favor or would even consider supporting a military coup (such as the 43% of Republicans) are almost always those who favor dictatorships in general (even if they usually lie about it), because they think the dictators will be members of their in-group who will look out for their interests. Sometimes this belief is naive stupidity of the sort that nearly every Trump supporter has that isn't a multi-millionaire but thinks Trump is part of "their" group. Other times this belief is actually rational because the person is in fact a member of the majority and/or weapons-controlling in-group whose interests will benefit from a physical fight for authoritarian control.