I've also seen subtropical defined as the "warmest parts of the two temperate zones."
The only climate type with the word "subtropical" in it is Humid Subtropical. In North America, the only place this climate is found is in the southeast quarter of the United States. And if you study the northern boundary of the climate type, it almost exactly follows the boundary of USDA Hardiness Zone 8a. Not coincidentally, it is Zone 8a where even the casual plant person begins to notice a variety of plants with strong visual (and genetic) ties to plants in the true tropics. Plants like palms, bromeliads, and agaves.
Many of these plants can also be grown west of the Rockies in areas designated Marine West Coast and Mediterranean Climate. So, are those places "subtropical", just without the name? I'm not sure.
My own definition of Humid Subtropical, as experienced in the eastern U.S., is this: A region of long, hot and humid summers with brief springs and autumns. Winters feature below freezing temperatures most years, but temperatures lower than 10F are very rare. Daytime high temperatures tend to average 50F or warmer in the coldest months. Snow is rare. Precipitation is spread out evenly throughout the year.
That's a pretty good, detailed, but concise definition. If anyone wants to add or subtract to that, be my guest.