Why is that an important distinction?

Seizing people and holding them for gain is...what?

Hundreds of Americans are kidnapped abroad every year. It's an illegal act; the host country virtually always works with the U.S. to sort it out. Backpackers kidnapped in Colombia don't necessitate diplomatic visits from high-up U.S. dignitaries for that reason.

Lee, Ling, and Yettaw's cases were totally different. They were arrested (arguably, rightfully -- all of them were trespassing) by authoritarian regimes with which the United States has no diplomatic relations.

So yes, the kidnapped and Lee, Ling, and Yettaw were all held for gain. But for what gain and by whom and under what circumstances? Of course the context is important.