Mason jars over the past century traditionally have had a two or three piece lid system. One of those pieces has always been a “ring” that screws onto the top of the mason jar in order to hold down the actual lid part during the canning process.
It appears that people working in the field prefer to call them “screw bands.”
- Ball: “Do not over tighten bands ”  https://www.freshpreserving.com/tools/faqs
- Bernardin: “Apply screw band – screw band down until resistance is met…”  https://www.bernardin.ca/pages/high_acid_foods_step_6_/62.php
- National Center for Home Food Preservation: “If lids are tightly vacuum sealed on cooled jars, remove screw bands”  https://nchfp.uga.edu/how/store/store_home_canned.html
- USDA: You can more easily detect some types of spoilage in jars stored without screw bands.”  United States Department of Agriculture (USDA). 2015. Complete guide to home canning. Agriculture information bulletin No. 539. Page 1-20
Here’s a screen cap from a Kerr Company manual from 1948, referring to the items as “Screw bands.”
It would appear, though, as the experts aren’t necessarily leading popular usage in this.
In January 2015, a Google Search on various terms produced these numbers:
- 411,000 hits on: “mason jar” bands  https://www.google.com/search?q=”mason+jar”+bands
- 866,000 hits on “mason jar” rings https://www.google.com/search?q=”mason+jar”+rings
- 975,000 hits on canning rings:  https://www.google.ca/search?q=canning+rings
That’s just a completely unscientific sampling, but it may show that the word “rings” is more popular than “bands.”
In any event, it’s difficult to imagine that there will ever be any mass consensus: you may even notice yourself using different terms at different times!
|↑4||United States Department of Agriculture (USDA). 2015. Complete guide to home canning. Agriculture information bulletin No. 539. Page 1-20|