The Kings have to finish the shortened resumed season in ninth place, and within four games of the eighth seed. Washington has to finish the shortened resumed season in ninth place, and within four games of the eighth seed. What's different about it?
If I understand the suggested format correctly...
In the Eastern Conference, there are three relevant teams. The Pacers and Sixers, currently tied for the 5th/6th slots in the playoffs cannot be caught and would be guaranteed playoff berths at the 6th seed or higher. Thus, the Nets, Magic, and Wizards would be vying for three spots (two playoff spots and a play-in 9th spot). At least two of these teams will "advance" and there is room for all three teams to "advance". The effective standings would be:
7. Nets -0.5 GB (so 0.5 games up)
8. Magic 0 GB
9. Wizards 5.5 GB
Since half-game changes in the standings would not be possible as all teams would play the same number of "regular season" games (8), the Wizards would have to
1) Gain 2 games on the Magic OR
2) Gain 2 games on the Nets in order to reach a play-in scenario.
It would be unlikely, but possible, that they could climb to the 7th spot and make the playoffs while avoiding a play-in entirely.
In the Western Conference, there are effectively six relevant teams. (In principle, Dallas could fall the the 8th spot by losing all of their games and Memphis winning all of their games, but that is so unlikely as to not merit consideration. Dallas has, for all intents and purposes, sealed the 7th slot at worst.) Thus, the Grizzlies, Blazers, Pelicans, Kings, Spurs, and Suns are all vying for only two spots (8th/9th). At most two of these teams will "advance". The effective standings would be:
8. Grizzlies 0 GB
9. Blazers 3.5 GB*
10. Pelicans 3.5 GB
11. Kings 3.5 GB
12. Spurs 4 GB
13. Suns 6 GB
The Blazers have a "record" advantage due to having played two more games than the Pelicans/Kings, and if percentage is used as the tiebreaker, would hold the tiebreaker over the Pelicans/Kings unless the tied teams both went 8-0, in which case there would be a true tie (both teams would be .500 exactly). In order for the Kings to reach a play-in game, all of the following would have to hold:
1) Kings must gain 0+ games on the Grizzlies AND
2) Kings must gain 1+ games on the Blazers (or go 8-0 and win tiebreaker) AND
3) Kings must gain 1+ games (or 0 games and win tiebreaker) on the Pelicans AND
4) Kings must gain 0+ games on the Spurs AND
5) Kings can lose no more than 2 games on the Suns.
The Kings could not climb to the 7th spot and avoid a play-in entirely.
So, while the goal is the same, the road is very different, and I would argue considerably harder for the Kings.
And, in lieu of doing things I ought to be doing, I ran a simulation. Assuming for simplicity that 1) all teams will have a .500 chance of winning each "regular season" game and 2) none of the "regular season" games are between teams vying for a final spot the results are as follows:
The Wizards would have about a 35% chance to make a play-in game.
The Kings would have about a 21% chance of making a play-in game outright and about a 6% chance of tying for a play-in game, so about a 24% chance overall of making a play-in game.
That's less of a disparity than I would have thought, but still a tougher road for the Kings.