It depends on how you got the bug. If you test something on your own machine and find a vulnerability, you're fine publishing it (modulo you may be civilly liable if a binding contract prevents you from doing that kind of research --- a pretty rare case). If you find a vulnerability in someone's SAAS application running on their server and publish it, the publication itself probably isn't unlawful --- the problem you'll have is that you've also published evidence that you committed a federal crime.

To be clear: I meant releasing an exploit, not a bug.

Per my understanding, there is a distinct difference between releasing a bug (that you found in software on your own machine) vs. releasing a tool that exploits that bug.

I don't really think that's true either, though obviously it has to be at least a little riskier to release an exploit; like, a fact pattern that has actually happened before is "someone writes an exploit, and a friend uses that exploit to steal a bunch of credit cards; the exploit writer is culpable as a co-conspirator". But just releasing an exploit by itself is I think --- NOT A LAWYER, TALK TO A LAWYER --- pretty safe.

This also comes up in discussions about exploit markets: you can sell an exploit to a bounty program, or to Zerodium or whatever, but people always think you can make more (for instance, if it's some dumb SQLI, more than the $0 the public exploit markets will pay you for it) by selling "on the dark web". But if you're selling a bug that only lets you exploit some specific SAAS application "on the dark web" to some anonymous criminal (or someone a jury will think you should have known was a criminal), you're taking a chance that a prosecutor will make a case that you took money to facilitate a specific crime that they're now going to charge you with.

Yeah, I’m not totally certain, and I suspect intent matters.

My example was that cracking a game is illegal, but releasing a cracker is much much worse.

And, again, IANAL.

Part of it is that there's a specific law criminalizing copy protection bypasses (the DMCA), but it also includes an explicit exemption for security research.

I am not a lawyer, but for example, cracking a game is against the EULA and likely illegal. Releasing a cracker is much worse.