I tried to read your post and it sounds like you are getting some of your terminology mixed up.
There are cartridges and then there are bullets. Too often I hear people refer to bullets as loaded cartridges. Reads like you are doing it too.
The 300 WSM doesn't fit your 300 win mag because a the internal dimensions of the chamber of your rifle was made to fit the 300 win mag. The 300 WSM is shorter but the diameter of the case is larger. Good thing it doesn't fit your 300 win mag.
Both cartridges shoot .308" diameter bullets.
The ONLY cartridge that should be fired in a rifle is printed on the barrel.
----------------------------
300win mag :
Bullet diameter
.308 in (7.8 mm)
Neck diameter
.339 in (8.6 mm)
Shoulder diameter
.489 in (12.4 mm)
Base diameter
.513 in (13.0 mm)
Rim diameter
.532 in (13.5 mm)
Case length
2.62 in (67 mm)
Overall length
3.34 in (85 mm)
300 WSM:
Bullet diameter
.308 in (7.8 mm)
Neck diameter
.344 in (8.7 mm)
Shoulder diameter
.538 in (13.7 mm)
Base diameter
.555 in (14.1 mm)
Case length
2.100 in (53.3 mm)
Overall length
2.860 in (72.6 mm)
I would suggest you get a reloading book made by Nosler, Sierra, Speer, or Berger. Read about the various cartridges and become more knowledgeable about the terminology.