Chow, pong and kong are together called claims — melds you expose by taking one tile another player discarded and pairing it with tiles already in your hand. The core differences: chow is limited to your previous player, pong isn't, and kong is four of a kind.
Chow: the previous player's tile + two connecting tiles
Only discards from the player to your left (your previous player) can be chowed, and you must hold two tiles that form a run with it. Say the previous player discards a 4 of Bamboo and you hold its 5 and 6 — chow it into a run:
Pong: two matching tiles + anyone's third
Hold two identical tiles, and anyone may discard the third — pong works from any player, not just your previous one. The completed triplet is laid open and counts as one meld. Two 7s of Characters in hand plus a discarded 7:
Kong: four of a kind, in three flavors
Exposed kong: you hold three identical tiles and another player discards the fourth — declare it open. Concealed kong: you collect all four in your own hand and declare it in your own turn, face down. Added kong: you already ponged the tile and later draw the fourth — add it to upgrade the pong into a kong.
The trade-off: a kong lets you draw a replacement tile (from the end of the wall), so it doesn't cost you a draw — but four of a kind could have been two pairs or two run-paths. Kong isn't automatically good; as a beginner, “pong freely, kong with a plan” is a safe default.
The cost of claiming: a concealed hand
Every chow, pong and kong breaks a fully concealed hand (a whole game drawn by yourself). Concealment is a scoring bonus in many rulesets and affects patterns like All Chows. Rule of thumb: claim when your direction is clear — random early claims tend to lock your hand into nothing.