also: kick · kick out block
A puller hits the edge defender from the inside and drives him further outside. The runner goes inside the block. It is the standard finish to a trap and to the playside pull on a buck sweep.
A pulling lineman arrives on the end man on the line of scrimmage from the inside and blocks him outward, away from the formation. The runner goes inside that block, in the space the defender used to occupy.
The blocker's job is to establish and keep inside leverage, which is what makes the lane. The technique detail that matters is that this is a collision on the move against a defender who is usually also moving, which is why it is taught as a distinct skill rather than as a block that happens to be far from home.
kicklog block, fan block, trapKick out names a target defined by ORDER rather than by position: the first man outside the hole, whoever that turns out to be. That is what lets one rule survive the defense lining up somewhere new. It is also why our own play assignments can say kick out the end man without naming a position.