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, trap blockKick out names a target by order rather than by position: the first defender outside the hole, whoever that is against the front. That lets the same rule survive a defensive alignment change.