The cartridge started out as the 6mm BR Remington, or 6BR Remington.
Then Norma took the cartridge and lengthened the neck a bit, and called the case 6mm BR Norma. When people use the term 6BR, today, they almost always mean 6mm BR Norma. Some people say Norma changed the body dimensions slightly, but a colleague of the original Rem designer says that's not true. From our measurements, it appears the Remington shoulder and case web diameters,as manufactured) may be slightly smaller--enough that Lapua and Norma-headstamp brass may not fit in a 6mm BR Remington chamber, even if the neck is trimmed to fit.
Anyway, the cartridge is now officially called 6mm BR Norma. But, the most popular brass is made by Lapua. Confused yet?
The only thing you really need to know is that if you have a barrel chambered, make sure your smith understands that 6mm BR Norma has a longer neck than the older 6mm BR Remington. AND, ideally you should use a reamer spec'd for CURRENT Lapua-headstamp brass. The Norma is pretty good, but most people believe that primer pockets will stay tight longer with Lapua.
I recommend you read the
6mmBR FAQ
Also this thread has the current Lapua case dimensions, as communicated to us a few days ago from Lapua R&D in Finland:
Lapua Factory Specs
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The one thing to really watch out for is that the 6mm Remington cartridge is COMPLETELY different. Different case altogether if there is no "BR" in the name.
If you stick with one of the smiths recommended on this site, and use reamers from a good operation such as Pacific Tool & Gauge, you won't have any problems. For your varminting purposes, we would recommend a .272" neck, and a 1:10 twist barrel. If you are using the gun exclusively at 500+ yards, get a 1:8 to shoot the high BC bullets.