And now for the long answer........ The Berea "B" mandrel is 0.291" in diameter which translates to about 7.4mm. There is a little tolerance in their mandrels so the "B" mandrel might be as small as 0.289". The "A" mandrel is 0.247" in dia.(about 6.3mm) and has the same under tolerance.
All of the bits of information posted previously are correct to the best of my knowledge excepting the speculative comment about both mandrels possibly fitting the same collet.
If you purchase a Berea High Precision "B" mandrel, you will need to purchase the matching drill driver. And that driver will "NOT" be compatible with the "A" mandrel which will require its own driver.
If you desire a little interchangeability, you can purchase the Berea precision mandrels. Both the A and B mandrels have the same 1/4 x 28 threading and can use the same arbor. I think the 1/4 x 28 threading is fairly standard and believe you can interchange arbors and threaded mandrels from different suppliers except for the threaded Woodcraft mandrel. It has a 10 x 32 thread and will not fit arbors than the woodcraft version.
Some folks like to use collet chucks like the Beall or the Axminster Jr. You will need a 1/4" and a 5/16" collet. Nice thing about the Beall collet is that it uses standard ER-32 collets which are widely available. The Axminster collets are ER-20 collets and probably readily available as well; but ER-20 collets are smaller and only go up to 1/2" gripping size. The ER-32 collets will handle 3/4" stock.
That's about all I know. Probably have missed a few things; but I'm sure someone will be along to help me out.