UPDATES AT BOTTOM
I suppose it could be called impeachment when a Congressional body ousts a sitting president via force. But it is not as simple as that.
A group of people in a Congressional body join forces and pressure the rest of Congress because those few have the backing of the military, which they then use to remove a sitting president from office and transport him to another country. That is the definition of a bloodless coup.
As noted here (in Spanish), the Honduran Congress cited repeated violations of the Honduran Constitution by President Manuel Zelaya and voted for his removal. That said, as I noted earlier, he is both a bad guy and a good guy. This is a complex political environment in a very unstable part of the world.
The right sees this as a simple restoration of democracy. Yet the use of military personnel to detain, arrest, and transport a sitting president to another country against his will is not part of any democratic process that I am aware of. They do have courts in Honduras and a legal system. This is a coup, despite the passions of the right-wing. They also have law enforcement. Anytime the military becomes involved, it is not as simple as impeachment by Congressional edict through military force. Shorter=coup.
Think on this...
As much as I disliked George W. Bush and Dick Cheney both, I would have screamed bloody hell if Congress - led by the Democrats - ordered the military to swoop down and remove both from office, dropping them off in Mexico against their will and named Nancy Pelosi the POTUS in a 24 hour period.
I would have been absolutely pleased if Congress had impeached both Dick Cheney and George Bush and a trial had taken place. That would actually be proof of a strong and vibrant democracy. Yet regardless of how corrupt both Bush and Cheney were/are and regardless of their abuses of power and the Constitution, I would still be against the use of military force to remove them from office and out of the country. I can only imagine how the right-wing would have reacted if a Democratic-led Congress enacted this in the US. They would be outraged and I would be standing with them. Would the right-wing, however, be outraged if Obama was removed by military force on the orders of a Republican-led Congress? Somehow I don't think so.
Regardless of how corrupt Zelaya was or was perceived to be as the leader of Honduras, an arrest and trial would be the proper method for his removal. The public would see the crimes and hear the testimony and justice would be served. Dropping Zelaya off in Costa Rica and not hold him accountable is not justice for his alleged crimes. It is simply a coup. By the way, I go to Costa Rica often. Being dropped off in any part of the valley, IMHO, would not be punishment. It is a lovely country with the cleanest air and water supply I have ever encountered. The Ticos are also extraordinary people. Seems like Zelaya got a vacation, not a punishment of any sort.
UPDATE I
Not only are some of the more extreme elements of the far right claiming this coup to be a victory for the Honduran people, they are also now claiming that the Obama administration is trying to undermine democracy by condemning the coup. Wow. How does one even begin a conversation with a person who cannot grasp basic principles of democracy? Just because someone (in this case, the people who ousted Zelaya) claims that there actions are legal, does not make it so. In fact, in every bloodless coup (and even most of the bloody ones), the people enacting the coup claim to represent the will of the nation and proclaim their actions entirely legal.
Again, use this example to better understand the absurdity of the "not coup" crowd:
Nancy Pelosi and the Democratic leadership order the arrest and rendition of President Bush to Mexico using loyalists to the Dem leadership in the US military to accomplish this process. Pelosi and the Dems then quickly assemble enough of a majority to vote on a hastily written bill of sorts. The vote declares that Bush is no longer president and that Nancy Pelosi is now the POTUS.
A resignation letter alleged to have been written by Bush is provided to the compliant media. Yet Bush, who is by now in Mexico, denies ever having written a resignation letter or resigning. Pelosi, Justice Stevens, and SecDef Robert Gates all tell you this is legal.
What would you call this situation if you were a Republican sitting at home watching Fox News? Hell, I am an independent and I would call it a coup. How difficult is it to understand why this coup is exactly that, a coup? Why would anyone claim this was the workings of a functional democracy?