In 1993, long before N. Korea had nuclear weapons much less the missiles to deliver them, Clinton said if North Korea developed and used an atomic weapon, "we would quickly and overwhelmingly retaliate . . . It would mean the end of their country as they know it." he said.

Two key points:
(1) N. Korea had no nuclear weapons so there was no chance it could strike preemptively with nukes at S. Korea, Japan and Guam.

(2) Clinton explicitly said the threat would be exercised only after N. Korea dropped a nuke on an ally.

Needles to say, times have changed, N. Korea can right now kill hundreds of thousands if not millions of people, and Trump has threatened to annihilate N. Korea for conduct short of N. Korea nuking one of our allies -- in other words, Trump has provided N. Korea with an incentive to strike with nukes preemptively, a risk that Clinton did not face.

Alt-right junk sites like to quote Clinton without providing his full statement or the context because most of their readers are not smart or industrious enough to check for the actual quotes and context.

(2) Obama never said anything remotely like Trump. Here's the strongest statement I could find, from 2016: "We could, obviously, destroy North Korea with our arsenals,” he told CBS News. “But aside from the humanitarian costs of that, they are right next door to our vital ally, [South] Korea."

I don't believe Bush said anything as inflammatory either though I have not done a thorough check. Here is a typical comment from him: "If North Korea makes the wrong choices, the United States and our partners in the six-party talks will respond accordingly. If they do not fully disclose and end their plutonium, their enrichment, and their proliferation efforts and activities, there will be further consequences. Multilateral diplomacy is the best way to peacefully solve the nuclear issue with North Korea. Today's developments show that tough multilateral diplomacy can yield promising results."