Pairs events, normally matchpointed, are the most common club format; Teams events compare two tables playing the same boards in opposite directions, normally scored in IMPs; Individual events change partnerships during the session (Law 4)
Source: Law 4, Law 81 — American Contract Bridge League — Laws of Duplicate Bridge
Why people argue about this
People often assume that in Individual events of Duplicate Bridge (ACBL), all players compete against each other head-to-head throughout the session, which isn't accurate. Actually, they change partnerships during the session as per Law 4, playing different boards with various partners rather than facing off directly against one another.