They come both ways.
Thre years ago I bought a Criterion knock-off, probably made in China, it works, does the job I asked of it, came with a number of cemented carbide tools, all of which needed touching up. While Criterion is arguably the industry standard, mine works as well as Criterions I've used in the past. For Hobby, work, save your money for additional tools
Thanks for clearing that up as i have no experience with that brand of tooling. My reply was a Generalized answer to the first part of the OP's question.As far as I know, Criterion only made the DBL-202 series in the threaded adapter configuration. They intended this to be something every shop could own so they made them with the 7/8-20 thread in back and then made almost every possible adapter to fit it. It worked, too.