Triton

Fish man. Merman?

Tritons (not to be confused with tridents) are a race of aquatic humanoids originating from Greek mythology, being followers/descendants of the original Triton, the son and messenger of Poseidon. They can essentially be summarized as "merfolk, but with a sillier name".

In Dungeons & Dragons, Tritons are distinguished from merfolk in that they have two lower limbs rather than one (originally two merfolk-style fishtails in lieu of legs in their 1e Fiend Folio appearance, thereafter changed to the less silly legs with finned feet look) and are more magical; Tritons originated on the Elemental Plane of Water, but have since migrated en masse to the Material Plane, to the point they are considered Native Outsiders in 3rd edition.

Tritons are fairly obscure, but they have been playable races throughout the first 3 editions, getting racial writeups in 1e's "The Sea People", 2e's "Sea of Fallen Stars" for the Forgotten Realms, and 3e's "Savage Species". This is because, unlike merfolk, the tritons' legs allow them to freely move about on land and in the water with equal ease, whereas merfolk are pretty much reduced to crawling like oversized slugs if you pull them out of the water.

AD&D

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3e

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5th Edition

Tritons are one of the playable races introduced to 5th edition in Volo's Guide to Monsters. They are very paranoid of other races, having spent the entirety of their lives underwater with little to no contact with the outside world. They act proud and noble, but are like fish out of water on the surface. Almost no one sees them or cares about what they do, so no one takes their proud boasting about their culture seriously. This can lead to tensions as your Mary Sue Triton gets humbled by surface dwellers who have no idea who he is.

Statline

Ability Score Increase: +1 Strength, +1 Constitution, +1 Charisma

Medium size

Speed 30 feet, Swim 30 feet

Darkvision 60 feet

Amphibious: You can breathe both air and water.

Control Air and Water: You can cast Fog Cloud once per long rest. From 3rd level, you can cast Gust of Wind once per long rest. From 5th level, you can cast Wall of Water once per long rest. All spells granted by this trait use Charisma as your spellcasting ability score.

Emissary of the Sea: Aquatic beasts have an extraordinary affinity with your people. You can communicate simple ideas with beasts that can breathe water. They can understand the meaning of your words, though you have no special ability to understand them in return.

Guardians of the Depths: Adapted to even the most extreme ocean depths, you have resistance to cold damage, and you ignore any of the drawbacks caused by a deep, underwater environment.

Kalamer Tritons

Keith Baker finally and officially merged tritons and merfolk together when he released his Exploring Eberron splatbook for 5e. Rather than being two races which are almost the same save for limbs, the Kalamer are aquatic humanoids who can shapeshift between a legged form, for exploring on land, and a tail-bodied form for better adaptation to life under the water. To play one, just take a triton, change the languages to the Eberron appropriate equivalents, and give 'em this extra racial trait:

Kalamer Transformation: When you finish a short rest, you can shapeshift from triton to merfolk form, or vice versa. Triton form functions as per the standard 5e triton. In merfolk form, your legs merge into a large, fish-like tail; your land speed drops to 10 feet and your swimming speed increases to 40 feet. You choose when you adopt merfolk form whether equipment and clothing worn on your legs falls away or is absorbed into your body until you resume triton form.

Magic the Gathering

They are also used in Magic:the Gatherings Theros setting. Here they are much more directly merfolk with legs with a funny name, as they are literally merfolk in creature type. Cosmology isn't particularly related to D&D's as they are not more extraplanar than any other humanoid.

The Races of Pathfinder
Player's Handbook:	Dwarf - Elf - Gnome - Half-Elf - Half-Orc - Halfling - Human
Advanced Race Guide:	Aasimar - Catfolk - Changeling - Dhampir - Duergar Drow - Fetchling - Gillman - Goblin - Grippli - Hobgoblin Ifrit - Kitsune - Kobold - Merfolk - Nagaji - Orc - Oread Ratfolk - Samsaran - Strix - Suli - Svirfneblin - Sylph Tengu - Tiefling - Undine - Vanara - Vishkanya - Wayang
Bestiaries:	Android - Astomoi - Caligni - Deep One Hybrid - Gathlain Gnoll - Kasatha - Munavri - Naiad - Orang-Pendak Reptoid - Rougarou - Shabti - Trox - Yaddithian
Adventure Paths:	Being of Ib - Kuru
Inner Sea Races:	Ghoran - Monkey Goblin - Lashunta - Skinwalker Syrinx - Triaxian - Wyrwood - Wyvaran
Ultimate Wilderness:	Vine Leshy
Blood of the Sea:	Adaro - Cecaelia - Grindylow - Locathah - Sahuagin - Triton
Planar Adventures:	Aphorite - Duskwalker - Ganzi