For many years, I had only one boolit sizer, RCBS. My assortment of H&I dies is a mix of Lyman and RCBS. Either brand of die fits into my RCBS sizer, completely interchangeable, or so it seemed.
Recently, I bought two Lyman 450 sizer machines, one from a local estate sale and another from eBay. Both were fixed up with some fresh parts and put into service with White Label lubes. I now have the RCBS and one of the Lymans set up with BAC lube for rifles and the other Lyman with 50/50 for pistols.
Only to find out that while Lyman dies will fit nicely into the RCBS sizer, the reverse is not true. Lyman dies and the hole they fit into inside the sizer are about .004" smaller than RCBS dies and sizers. Reminds of the Russians and their 82mm mortars, they can use our 81mm rounds but we can't use theirs.
All of this is probably well known to the old hands here, but I'm now learning it the hard way. Just wanted to commiserate. - CW