Well, from what i know, Level Designer and Game Designer are 2 different roles, especially for triple-A titles. Mods, maps and prototypes are the best stuff to show LD's capability. As for "pure" designer like GD, I do believe that shipped projects you previously worked on can prove your value.
Sometimes people tend to promote their own employees instead of hiring a game designer from the outside. Things might be a lot different for MMO and casual games.
Correct me if I am wrong.
Level design is a subset of game design and the same skills apply, on large projects you tend to have a lead designer who is responsible for keeping things coherent and then a group of people responsible for various aspects of the game, none of these aspects are more pure than the others though. (This is no different from how programming and art are structured on most large teams, once you have a group of people working together companies tend to put someone in charge of that group to ensure that everyone is pulling in the same direction), For indie teams you rarely have multiple people in one role(usually you have one person in multiple roles instead) so things won't be broken down as far and people don't tend to specialize as heavily.