Any time you upload data to your account as a tileset, it is given a map ID. Map IDs are also used to identify projects created with the legacy Mapbox Editor and styles created with Mapbox Studio Classic.
Map IDs will always start with your Mapbox username followed by your tileset's unique handle:
username.handle. Note that styles made in the Mapbox Studio style editor and datasets uploaded to Mapbox Studio or created through the Mapbox Studio dataset editor do not have map IDs -- they are identified with style URLs and dataset IDs.
You can request tilesets directly using the Mapbox Maps API.