The bullets are the same. .429 diameter. .444 uses a 260 grain in factory loads. Little heavy for the mag pistol but doable... Any pistol bullet could be used in the .444 loaded into the .444 cases appropriately.
As said, the 444 is bigger around at the base. If you were able to get a .44 Mag to fire in the chamber and the settling in the larger hole might misalign the firing pin, IF it fired, then the case would probably split releasing hot gases. The hot gases' pressure determines temperature. (Boyles law??? Long time since chemistry.) I think 40,000 pressure equals temps of 3,000 degrees. A cutting torch operates at 2,000 degrees. The amount of gas is small but if it reaches critical parts holding the gun closed and they "melt" or just lose strength from the heat... No telling what might "come back" at the shooter...not to mention "bits" of case brass or powder for that matter. If you are lucky, you are DEAD. Something reaches the brain. If not, you might lose an eye (or two) and the side of your head needs "reconstruction..." Not cheap or pretty or fun... So please don't. This is the sort of thing the media uses to make all shooters look like stupid criminals... luck