the radial pin and the 3/8x10 pin are part of the big pin family in my opinion along with other like the southwest pin . the way to read a thread by the numbers and see if it will fit goes as follows
example
3/8x10
3/8 is the pitch of the thread , the inclination.
x10 - how many threads are per inch. if you would take a 3/8x10 pin and cut exactly a inch you would have approximate 10 rotations or the thread.
as you can see from the picture about the 3/8x10 has a little more threads per inch then the radial pin which is approx 3/8x8. The pitch is the same but the number of threads is less.
other common threads are
5/16x18
5/16x14
southwest - 3/8x11 - same pitch more threads per inch.
so technically the pitch matches between the radial pin and the 3/8x10 pin the the number of rotations does not. if you try to screw it on and force it , eventually it will screw in but you will destroy the wood threads.
personally i love the radial pin - easy to install accurate as a cue maker and as a player i love that i have even more flat contact with the wood. my personal favorite.
Enigmatical, I think you've got a few things mixed up.
The 3/8 function is the diameter of the pin. It's not always exact, as the "topping" of the threads can take it down some. So, a 3/8" pin will typically measure somewhere from .365" up to .375" or so.
The 10 function is the number of thread peaks or valleys in 1" of length. So a 3/8-10 thread will have 10 thread in 1" of length, or 5 threads in 1/2" of length, etc.
The pitch is the length of 1 thread, or the distance the screw will move with 1 turn. The pitch is the number of threads per inch divided into that 1". So, for example, a 10 thread per inch screw will have a .100" pitch. There is .100" between each thread, and it will move .100" if you turn it one revolution.
For the OP, the only real difference between a 3/8-10 and a 3/8-8 is the threads per inch or the pitch. As Chris has already stated, just try to screw the shaft on lightly. If it start to get tight after about a 1-1/2 to 8 turns and just gets tighter, then you have the wrong one.
I hope that helps!
Royce