Halloween Is Grinch Night/WMG

The Cat Grinch is a different Grinch from the one in Whoville.
Max could have been passed to The GN/HTGSC Grinch. The Grinch Night take place the same year as Christmas, and he stole Max back in between.
 * I always assumed "Grinch" was a species, or at least a family line.

There are multiple Grinches.
The Grinch from Grinch Night is the Grinch of another Whoville. Hey, there are probably hundreds of specks out there, each with Whovilles, and each with grinches. The How the Grinch Stole Christmas Whoville is different from the Halloween Is Grinch Night Whoville, the Horton Hears a Who Whoville, and the The Grinch Grinches the Cat in the Hat Whoville. It's like parallel universes. Each one has a Grinch (who has a dog named Max). This accounts for the different voices, Negative Continuity, and the fact that Max can talk in this one.
 * The Horton Whoville is a speck in a jungle. It has a nicer Grinch (one Who in the film looks like the Grinch, he could be the town's local Grinch) and a democratic system. Max is never seen, so it can be assumed this Grinch doesn't have a dog.
 * The Grinch Night Whoville is a speck caught in a windstorm. Its Grinch is sadistic (Grinch is gonna get ya! Grinch is gonna get ya!) and meaner than the others, is Always Chaotic Evil, and the dog stayed with Euchariah for the rest of his days.
 * The Christmas Whoville is a speck stuck on a snowflake. Its Grinch used to be evil, but now is nice. Max stayed with his newly-reformed owner, the Grinch.
 * The Cat Whoville is another speck entirely. This one has the Cat in the Hat, and has Jumped the Shark. I haven't seen it, so if there is a Max in it, he is an entirely different Max.

Everything takes place in the same universe to the same Grinch.
There is no Negative Continuity if some major events occur offscreen.
 * During Halloween Is Grinch Night, the Grinch is at his meanest and is not redeemed at the end. After Max goes to live with Euchariah, the Grinch cooks up a scheme to get Max back and succeeds. (Or he gets a new﻿ dog and names it Max, possibly one of Max's puppies, making it Max Jr.)
 * The Grinch is redeemed during How the Grinch Stole Christmas. A while after the events of this story, the Grinch and Max move off the mountain to a new lair; possibly because it's harder to drive his new snazzy purple car up to his old cave.
 * The Grinch Grinches the Cat in the Hat. The Grinch is mostly kind now, as seen at the beginning of the short, but old habits are hard to break. He hasn't fully integrated into society, and some days his past self comes back to him through the mirror. However, with the Cat helping him out as seen at the end of the short, the Grinch may be less likely to fall back to his old ways.