It comes down to the difference between stealing information and directly causing widespread death and/or destruction.
America lets the Chinese army get away with hacking into and stealing secrets from a slew of giant multinational corporations because hacking is just another form of espionage, and espionage is not an act of war.
Countries have been conducting espionage against each other for thousands of years, and though spies have been caught and killed, generally their spying hasn't led to a war.
It's pretty much assumed that every foreign embassy has intelligence personnel working inside it. In fact, Americans have made several concerted attempts to bug the Russian Embassy in the U.S. (and vice versa).
What makes China a bit different is that they're apparently doing it so well. Companies are obviously being robbed, but there's also the possibility of hackers perpetrating real-world damage — the threat of damaging critical infrastructure and lives in the process.
Actual real-world damage, it turns out, is where the international community draws the line. Researchers and military professionals recently got together to sort out the whole idea of using military might against a sponsoring country or a collective of cyber hackers.
From Global Post:
The so-called Tallinn Manual, published in March, controversially concluded that nations would be in their rights under international law to respond with bombs or bullets against cyber attacker that caused death, destruction or damage on a significant scale.
We also talked to Jarno Limnell, a cyber security expert at Stonesoft, who told us via email, "the cyber espionage that has been making headlines recently should not be counted as warfare or as an act of war."
Limnell concluded with a warning:
"The ability to escalate from espionage to destructive cyberwar is certainly there, but fear may ultimately perpetuate this eventuality. It is possible, for example, that the ongoing 'cyber spying accusations' between US and China could escalate to real war, especially in a climate of mutual distrust and fear."
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