1) Do not BLINDLY force on the cog. Check out its threads, see if there is a burr or other problem with them.
2) While there are 3 Major different thread standards(+French), they are similar enough that people swap between them without major issues.
Originally Posted by Baxtefer
Type Thread Equivalent
I.S.O. 1.375" x 24 tpi 34.92 x 1.048 mm
British 1.370" x 24 tpi 34.80 x 1.058 mm
French 34.7 x 1 mm 1.366" x 25.4 tpi
Italian 35 mm x 24 tpi 1.378" x 1.058 mm
and
ISO, English and Italian are all semi-interchangeable, but it you shouldn't go back and forth between different types of freewheels on the same hub repeatedly
3) Lockring threads are where there is the drastic difference between "regular" and Campy/Miche/Phil.