Bullet diameter, case length.
Projectile diameter.
The 44 Magnum case is a little longer.
I'm not aware of a .45 Magnum. There is a .44 Magnum. The 44 magnum is typically a revolver round, very high power. The 45 ACP is typically used in semi-automatic pistols. The 45 ACP is not as powerful compared to the 44 magnum (mostly due to the amount of propellant in the 44 magnum compared to the 45 acp).
Chamber pressure for one.
A 44 magnum is just the new and improved version of the 44 special which the special is a 44 caliber. Magnum just means bigger so the 44 magnum is pretty much in between 44 and 45 cal. However, if you mean size, .45 is slightly larger in diamater than .44.
.44 Magnum
Caliber refers to the size of the bullet in the cartridge, or the size of bullet the gun is designed to fire. Magnum refers to a cartridge with a higher level of pressure/powder than another one similar to it. For example: a .44 magnum has a longer casing and more powder than a .44 special.
In a .44 Magnum revolver, yes. In a semi-automatic .44 Magnum (such as the Desert Eagle), no.
.44 Magnum has a longer case, more powder, and higher pressures generated.
It can use either 44 magnum or 44 special
Yes. The 44 magnum can fire 44 special ammo in the same way a .357 magnum can use .38 Special.
There ARE rifles and revolvers chambered for the 44 magnum cartridge. If the weapon is marked ".44 Magnum" then it can be used in that weapon. You should know that there are other .44 caliber catridges, and THOSE weapons (44 Special, 44-40, etc) cannot use 44 magnum loads.