A commercial vessel, registered, licenced and operated under the laws of a specific flag state. (Draft based on Wikipedia). Every State shall effectively exercise its jurisdiction and control in administrative, technical and social matters over ships flying its flag (Source: UNCLOS, Art. 94.1)

Flag vessel in the context of CMS: "Range State" in relation to a particular migratory species means any State [...] that exercises jurisdiction over any part of the range of that migratory species, or a State, flag vessels of which are engaged outside national jurisdictional limits in taking that migratory species (CMS, Art 1h) (Source: CMS)