Runner on 1B. Batter hits the ball through the infield to the right fielder who throws the ball to the first baseman in an attempt to put out the batter-runner, but throws it out of play. Prior to the wild throw, the runner from 1B arrived at 2B but the batter-runner had not arrived at 1B.
Result: Runner scores and the batter-runner gets 2B. (Rule 8.4(10).D).

Same scenario, except the ball is hit to the shortstop.
Result: Runner gets 3B and batter-runner gets 2B. (Rule 8.4(10).E.1).
Why does this rule differentiate between a ball hit to an outfielder and a ball hit to an infielder?

From what I can recall from umpiring decades ago, out of play throws from an infielder reverts back to where base runners/batter are at the time of the last pitch. From the OF, where was the base runner's/batter at the time the ball is released by the OF. A fast batter could have already touched first base before the release. If there is a double play attempt by the infielders, it is based on the position of base runners/batter at the time of the second throw.

Scuba, on that grounder to short was Usain Bolt on first base? 🧐

SCUBA,

First scenario: you place the runners from their last legally obtained base on the TOT (time of throw) by an outfielder.

Second scenario: you place the runners from their last legally obtained base from the TOP (time of pitch) on the first throw by an infielder.

Runners must touch all bases in their order. Subject to so, they can be called out by proper appeal.