As the other comment said, the MCC was a remaster. Most of the changes were cosmetic, to the point where it actually had a button to switch between original and remaster graphics, since it was the original engine running everything. The level design, mechanics, weapons, and such were all untouched.

The new Halo remake is a completely different game made in Unreal 5. Already from what has been shown it is very divergent from the original in many ways. This announcement is an intention to do that for the other games.

No. MCC mostly just ported the games to newer hardware and to PC. They eventually updated the game logic to operate at 60 ticks per second instead of 30 and added some new customization options, and it included from launch the graphical remasters of Halo 1 and 2, but it was really just ports and patches with a unified launcher.

What they're doing now is remaking the Halo 1 campaign from the ground up. New engine, new code, redesigned levels, new levels, etc.

Pretty much. But this new one is being done in a new engine (Unreal) and a lot of it is being done by AI. Two things that weren’t being done before, certainly on the MCC.

MCC was a remaster, this is a remake.

Im not sure it actually changed much except making it play nicer with modern windows.