There does seem to be a lot of confusion about the difference between the American cartoon case, and the Danish one. I suppose that's natural; both cases involve cartoons that offended people, and both have resulted in protests. That is where the similarity stops, however.
The key difference between criticism and censorship is whether the effect of the speech is to exchange ideas, or to silence opponents. In deciding which you are looking at, you have to look first and primarily at the context of the remarks.
Sovay mentions a similar case in Russia, to draw attention to what she views as the chilling effect of the JCS letter in protest to the Toles cartoon. The context for a letter from the Russian military expressing its displeasure is this: you might vanish in the night if you don't heed their friendly advice. No matter how gently worded, such a note is effectively censorship.
Similarly, the Muslim protests have involved threats of violence, and actual violence: bomb threats, rock attacks on the Danish embassy in Jakarta, threats of beheadings, flag burnings. The context for these remarks is the French riots, the Van Gogh murder, and a worldwide terrorist movement that cites Islam in justifying extraordinary violence in the name of Muhammed. All of this is censorship: an attempt to silence through threats.
The effect is real: a French editor who republished the cartoons was fired; the Danish newspaper remarks that no Dane (and indeed, no European in all likelihood) will draw Muhammed for a generation. The US State Department has even ruled that speech is unacceptable if it mocks Muhammed. Silence is enforced.
The context in the American case is completely dissimilar. Any observer should be able to tell the difference, which is this:
The effect of the JCS letter to Toles will be to increase Toles' wealth and importance as a speaker. Far from silencing him, it will raise his stature: he is now the only editorial cartoonist ever to receive a letter of protest from all members of the Joint Chiefs of Staff. The book he publishes with this cartoon in it will almost certainly outsell any other he has ever produced. That is the way America works.
Cassandra had a post about this recently. She was remarking about the recent flame-war attacks on the Washington Post ombudsman. The attempt, here, was to silence the Post -- it did not work. The Post was able to simply pull its comments section and carry on printing. If anything, it won the Post some sympathy and support from bloggers normally not on their side.
In the comments to Cassandra's post, however, I noted this about the flame-war organizer:
I looked at the Fire Dog site too. (By the way, it's almost the Chinese New Year; and this will be the year of the Fire Dog).And that is true. The Muslim protestors and Fire Dog Lake are similar in that their anger and violent rhetoric have caused their status to rise. They are taken more seriously than their ideas merit be because they are able to channel and direct anger.
What I noticed about it was the post where her site has suddenly rocketed to the very top of the Left blogosphere -- she's in company, according to that ranking, with Daily KOS, TPMCafe, and Atrios.
KOS himself, by far the most popular blog in the world, arrived at his fame as a result of the "Screw Them" comments. The thing that drove him to the top was, in other words, precisely his assault on the character of US veterans who had died attempting to aid their government in a time of war.
The market is what it is. As long as this is the way to rocket from nobody to THE BIGGEST THING EVER in a single day, we'll see more of it.
The criticism of the JCS, like the criticism directed at KOS and Fire Dog Lake, is actually a boon to the criticized. It raises their status, because serious people -- the Joint Chiefs! -- are willing to respond to them directly.
This is a result of the old truism that a gentleman duels only with equals. By replying to Toles, the JCS suggested that he was worthy of their notice and reply. They raised him to a status he did not previously have. Similarly, by being sternly critical of KOS' despicable statements and character, the entire right wing of the blogosphere declared that he was worthy of a response.
When exchanging ideas, it pays to be careful with whom you exchange them. This is why Grim's Hall never links to KOS or his ilk; I use them as examples, but I will not talk to them. They are unworthy of it.
It is also why I actually do practice a kind of criticism approaching censorship in my comments section, as (now) does the Washington Post. If you obey the rules, any idea you have to put forward is welcome. You won't be shouted down, because attempts to shout you down will be deleted. But you will have to argue your point based on reason, experience or evidence, so be prepared for that.
Your freedom of speech is not thereby compromised, however: you can go and publish your own blog, for free. As a result, even the deletion of comments is not censorship, because the context of it is that you are just as free as I am to express ideas. I'm simply refusing to allow my forum to be hijacked.
The American system results in raising some unworthy characters to the top of the pile on occasion, but it is still the better system. We will not be silenced, even the worst of us.