The tropics exist between the Tropic of Cancer and the Tropic of Capricon. The Equator is totally within the Tropics.
There are climatic types that are named after these zones.
While generally referencing the latitudinal zone between 23.5° and 34.0° in either hemisphere, bordering the tropical zone, subtropical can also refer to vegetation, organisms, or weather typical of subtropical habitats, and is commonly used in this context. For example, subtropical vegetation is identifiable in equatorial locales at high altitudes.
As you note -- "There are climatic types that are named after these zones."