Red drum are 'game fish' and cannot be harvested for sale in Louisiana. Restaurants that have red drum are getting them from other sources like farm raised fish, other states or countries that might still fish them commercially, etc.
(67) 'Game fish' means all of the following species of freshwater and saltwater fish:
(a) Freshwater game fish means largemouth bass (Micropterus salmoides), spotted bass (Micropterus punctulatus), shadow bass (Ambloplites ariommus), black or white crappie (Pomoxis nigromaculatus, P. annularis), white bass (Morone chrysops), yellow bass (Morone mississippiensi), striped bass (Morone saxatillis), hybrid striped bass (striped bass-white bass cross or striped bass-yellow bass cross), and any species of bream (Lepomis sp.).
(b) Saltwater game fish means any sailfish (Istiopharus platypterus), blue marlin (Makaira indica), black marlin (Makaira nigricans), striped marlin (Tetrapturus audax), hatchet marlin (Tetrapturus spp.), white marlin (Tetrapturus albidus), and red drum (Sciaenops ocellatus).http://legis.la.gov/lss/lss.asp?doc=105209
Spotted sea trout are not 'game fish'. They are harvested commercially in Louisiana for sale and can be found in restaurants.
Not going to copy this text from the law but, it explains how the Louisiana Wildlife Commission establishes the commercial quota for spotted sea trout taken by rod and reel in Louisiana.
There are also other sources of spotted sea trout from other areas where they are still commercially harvested.