Cold rolled is probably purely mechanical and all the ratios are probably done by CNC
Cold Rolled threads are all mechanically rolled through dies they create thread form. Unlike cut threads these have a radius. They are automated machines - not true CNC, blanks are fed in then the thread is rolled, ejected, then next part fed in. This process of rolling threads are much stronger due to the fact they realign the grain and get rid of the shear lines that cut threads create when they cross-cut the grain.
I’ve never seen a forged thread operation - it would be difficult to produce because where the forging dies come together there is a line produced which would act like burr every 180 degrees. Now very high tensile strength bolts may have the blank to be threaded produced in an upset/extruding single hit which would form the head and the radius at the top of the shoulder. My guess would be most bolts blanks are produced through a heading process that is fed from a coil - which can do hits in less than a second so volume is produced efficiently.