That is not correct in most places. A regular fishing license is not enough
Well, we already heard from Texas, here is Florida (That covers most tropical fish states in the US):
Requirements for Recreational Marine Life Harvest
■Recreational saltwater fishing license
■Organisms must be landed and kept alive
■A continuously circulating live well, aeration or oxygenation system of adequate size to maintain these organisms in a healthy condition
■
State regulations for marine life apply in federal waters
■Allowable Gear" : ■Hand collection
■Hand held net: a landing or dip net. A portion of the bag may be constructed of clear plastic material rather than mesh.
■Drop net: a small, usually circular net with weights attached along the outer edge and a single float in the center, used by a diver to enclose and concentrate tropical fish.
■Barrier net (fence net): a seine used beneath the surface of the water by a diver to enclose and concentrate tropical fish. The net may be made of nylon or monofilament.
■Slurp gun: a self-contained, handheld device that captures tropical fish by rapidly drawing seawater containing such fish into a closed chamber.
■Use of quinaldine is prohibited.
■Use of power tools for harvest of octocorals is prohibited
■Bag Limit: 20 organisms per person per day; only 5 of any one species allowed within the 20-organism bag limit unless otherwise noted. See charts below for more details.
■Possession Limit: 2-day possession limit, 40 total organisms, no more than 10 of any one species allowed.
■Allowable substrate: see species specifications in tables.
■Various closed areas exist. See regulations for Florida Keys National Marine Sanctuary, Everglades National Park, Biscayne National Park, national wildlife refuges and Florida's State Parks before collecting in these areas.
■Sale of recreationally caught marine life organisms is prohibited.