Chain association
One player says a word, the next player says a word linked to it, and the chain keeps moving: moon, tide, surf, board. The fun is in the drift, because after 10 words the chain can be nowhere near where it started. Chain association is usually played out loud or in a group chat, with no timer and no score.
Single-round same answer
Everyone gets the same prompt and writes one word without discussing it, then the group reveals and sees who matched. It is the shortest version of the format and the easiest to referee: either the words are the same or they are not. SameWord is this format with a clock, 5 rounds and a score.
Alternating word chaining
Two players take turns adding to a chain, but each new word has to follow a rule: same first letter, same ending, same category. This version is closer to a puzzle than a conversation. With a strict rule the game lasts longer, and a loose rule turns it back into free association.