You seem to be struggling to understand the difference between the two definitions of tropical here, but that's ok it can be kind of tricky:
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The high mountain environments of the Andes and deserts found between the two tropics are geographically/astronomically "tropical" according to definition 1
However, they don't meet the criteria for temperature or moisture to be "tropical" climates, even though they are geographically within the tropics. Here's a map of tropical climate zones, inclusive of tropical rainforest, savannah and monsoon zones: