There are many terms for "level" nowadays, depending on the genre of the game and also the preference of its designer(s).
Level typically means a secluded, in itself complete portion of the game, mostly independent of the rest; when I hear level, I think of 2D platformers exclusively.
For the first or third person shooter genre, levels are more typically referred to as maps. Maps are still technically secluded from the rest of the game - maps typically have a clear objective and transition between them is not seamless and requires significant time to load the next map. This implies greater freedom of movement and ability to backtrack at will, which is often significantly greater than in side-scrolling games.
For the sandbox shooter sub-genre, there is only one map, so it is more accurately referred to as world, as you already wrote, which implies the greatest possible freedom of movement.
As always, there are games that mix up the designs - for example, Wolfenstein (2009) had secluded, stand-alone maps with defined objectives, but they were connected by a "hub" map.
That being said, you could name the designer level, map, and world designer, respectively, but there is no standard set in stone - if someone said "I am a level designer for GTA", it would be understood.