Yep, tap holders for tapping heads. The little rubber collet inside cost BIG $$$ for what you get but they don't work well without it.
I'd stick with 5c or the er40 collets. I've used those rubber collet chucks and they don't hold well at all. But I've never had a metal collet let the piece move in side . Just my contacts with them years ago.Yup, those Jacobs rubber flex style collets are expensive & can be hard to find. If buying a tool that uses them be sure that it comes with them. My Tapmatic uses these types of collets, luckily mine came with them.
I've been keeping my eye out for a Jacobs rubber flex collet chuck for my lathe but they are hard to find for what I need. Hopefully one day.
I'd stick with 5c or the er40 collets. I've used those rubber collet chucks and they don't hold well at all. But I've never had a metal collet let the piece move in side . Just my contacts with them years ago.