I'm not surprised, as the Wall Street Journal reports, that the US government has been delaying and agonizing over what more to say about air strikes that killed two dozen Pakistani soldiers last November. The US promptly expressed "regret," but the Pakistani government wants a formal "apology" along with other acts of contrition and compensation.
American political figures really hate the "A" word. Mitt Romney has a major campaign theme alleging that the Obama administration is apologizing for just about everything. No doubt that's a strong reason the administration doesn't want to use the "A" word itself.
What's the difference? It must be powerful, since those politicians who do use the word still use formulations that deny any personal responsibility: Romney himself dealt with verified reports of a high school hazing incident by saying," I did some dumb things. And if anybody was hurt by that or offended, obviously I apologize." He apologizes for the reactions of others rather than for his own behavior.
Words matter. But I think we're going too far in trying to take synonyms and put them on a rickety ladder.