I have die sets from C&H that came in a fiber counter display box, at the time they were in El Monte, California. C&H printed the instructions in the bottom of the box. The instructions suggested the dies should be used with a shell holder with a height of .125".
I measure the deck height of shell holders, most of my shell holders have a deck height of .125". And then there are differences between shell holders, because of the difference between shell holders it is worth it to me to have shell holders that are no longer maid At one time there was a reason for the difference, how the shell holder is used is up to the reloader.
Some insist on matching manufacturers as the OP. I have three different sets of RCBS shell holders. One day I called RCBS with a problem, new shell holders would not fit my old equipment. They suggested I send them my 'old' shell holders for an exchange as in one for one. I suggested I could modify my equipment to fit new shell holders, I thought that would be easier and I explained to them a few of my old shell holders were unique because the deck height was not .125".
And I could modify my old shell holders to fit new equipment.
F. Guffey