When Egyptian military chief Abdel Fatah al-Sissi went on Egyptian TV Wednesday to read the statement that ended President Mohamed Morsi's one-year tenure, observers within and without Egypt seemed to hear one of two very different events.

Some, often those who opposed Morsi and saw his rule as increasingly undemocratic, cheered at the announcement that he would be replaced by the head of the constitutional court until early elections could be held. They saw the will of the people, expressed through mass protests numbering perhaps in the millions, finally fulfilled. But others saw a nation's fate decided by a khaki-clad general, a military coup under the veneer of popular support. And, for them, a few words in Sissi's statement jumped out in a way that it may  not have for others: "the constitution is suspended."

Debates are already raging over whether the events of July 3 can be fairly described as a coup or not, as the subversion of democracy or its expression. Those debates are largely academic; what happened could be said to meet the definition of a coup, as well as that of a revolution. But even though both words might apply, neither is in itself enough to describe what happened: It was both a coup and a popular movement, both the expression and subversion of Egypt's democratic experiment. And, as Foreign Policy's Joshua Keating points out, although some academic literature finds that coups can be democratizing that doesn't make them democratic.

But it's not easy, especially for those Egyptians who have invested and lost so much in their country's struggle since January 2011, to see both sides. Many, particularly Morsi's supporters within the still-vast Muslim Brotherhood, will likely see July 3 as little more than a military coup, the return of decades of military rule that always loathed the Brotherhood. Activists who opposed Morsi will surely continue to insist that the military stepped in only to safeguard the people's will from Morsi himself.

Few Egyptian activists invested in Wednesday's events on either side of the political spectrum will likely want to acknowledge the breadth of what happened – much as few have been willing to acknowledge both that Morsi possessed the mandate of a popular democratic election and that he had eroded much of that mandate by his own actions. Yes, the United States continued to deal with him and to describe him as the democratically elected leader; yes, he at times undermined democratic institutions and often excluded non-Islamists, neither of which did much to live up to the mandate Morsi often used to justify his behavior.

It's a cliche within U.S. politics to point out that the two ends of the political divide see different versions of the same reality and will never be able to accomplish anything until they can find a middle ground. But, in Egypt, this is deadly true, with one important distinction: The two "sides" to this political dispute are seeing the same reality – they're both right – but each is only able or willing to look at half.

That leaves the other half to imagination, and both Morsi's supporters and detractors had turned increasingly to conspiracy theories to explain the situation. Many in Egypt's opposition, unwilling to acknowledge any scrap of legitimacy for the Morsi government or the possibility that he enjoyed some real base of support, blamed his perseverance on clandestine American support. And Morsi's government, ironically enough, accused U.S.-funded NGOs of fomenting the Egyptian opposition movements, which Morsi seemed unwilling to believe could be rooted in legitimate gripes.

So, were the events of July 3 a coup, or were they a second iteration of the February 2011 revolution? Was democracy expressed, or was it subverted? The answer is "both." If Egypt is going to deal with this transition much better than 2011, it might well require both sides of this week's stand-off to acknowledge the full extent of July 3 and how the country got to that point. The Muslim Brotherhood, which is influential enough that it will likely remain a real political force, has some significant lessons to learn about political inclusion and legitimacy; it would not be easy for the group to ask itself if it really did squander its presidency, but they've endured much harder times than this.

A lesson for opponents of the Brotherhood, though, may be that the Islamist group didn't get to the presidency by accident and will not disappear. The Muslim Brotherhood has proven one of Egypt's most organized and effective political organizations. For the military and other to treat a coup that deposed the Brotherhood's president as a non-coup and democratic event leaves the Brotherhood little real space in Egyptian politics. That would seem to risk a repeat of the same problem that plagued and ultimately ousted Morsi – except instead of an Islamist ruler acting as if non-Islamists had no right to participate, it would be the other way around.

Similarly, to insist that what happened in Egypt was not a coup would leave the door open for the military to depose any ruler it feels has lost sufficient political legitimacy; even if you think the generals got it right this time around, will you still agree next time?

Flash back to February 2011, when cheering crowds received the news that President Hosni Mubarak was leaving office. It wasn't until several months later that observers started to wonder if it had really been a revolution that had toppled Mubarak, or a military coup. His resignation, after all, had been announced by one of the top generals who soon took interim rule. Tanks had been in the streets. Were events primarily driven by popular will, as expressed by thousands or millions of protesters, or by the powerful military?

That distinction is not much more obvious today than it was then. And, unless something changes in the Egyptian political culture that allows one part of the country to see two dramatically different versions of the same event, it's a distinction they may end up revisiting.