.300 win mag vs a .308 caliber
Let's get some terminology straight - strictly speaking "caliber" refers to the diameter of the bore, so the 300 WM *is* a .308 caliber cartridge because it - and several other cartridges - use a .308 bore diameter.
There is another cartridge called the 308 Winchester, often referred to as "308". This may be the source of your 300WM and 308 interchangeability question. The 300 WM and 308 Win are NOT interchangeable.
The 300 WM fires the same weight projectiles roughly 350 fps faster than the 308 Win. This generates considerably more recoil, enough of a difference that many people prefer to shoot the 308 unless the extra velocity / flatter trajectory / more power of the 300 WM is really required.
In a sporter weight rifle the two cartridges have similar accuracy depending on the degree to which the shooter can deal with the extra recoil of the 300 WM. This will vary considerably from shooter to shooter.
In an all out target rifle at short range the 308 Win would be slightly more accurate.