There are two different methods for creating maps with Mapbox tools: the Mapbox Style Specification and CartoCSS. The two are unrelated and incompatible – the tools that work with one do not work with the other.
Mapbox Studio Classic and Mapbox.js, on the other hand, rely on raster tilesets and GeoJSON vector data for map creation. Styles are created in Mapbox Studio Classic using CartoCSS and rendered server-side to create raster tiles. These raster tiles can then be added as tile layers in Mapbox.js.