recycling:cartons=* vs recycling:paper_packaging=*

Checking the history of the amenity=recycling wiki page, the recycling:<material> tags date from the early days of OpenStreetMap (the page was started in 2006). I suspect that for a time people were trying to map recycling and come up with suitable tags where there weren't any suitable on the wiki page.

recycling:paper_packaging was added on 5th January 2009 with the comment "(paper pacaging is a seperate recycling category in Iceland. Adding because I'm using it in the Reykjavík area)"

recycling:beverage_cartons was added on 11th June 2009 with the comment "Materials: beverage cartons" and a description of "Paper Based Beverage Cartons"

recycling:cartons was added on 18th January 2010 with the comment "Materials: UK recycling categories compleated http://www.leics.gov.uk/index/environment/waste/recycling_household_waste_sites/wastesite_loughborough.htm"

The modern version of that last link is probably https://www.leicestershire.gov.uk/environment-and-planning/waste-and-recycling/how-do-i-dispose-of and what they list under Cartons is the Tetra Pak style cartons which the wiki now gives as an example next to beverage_cartons.

So my personal interpretation is that if it is just paper based packaging, use the paper packaging tag, but if it is the tetra-pak based waxed paper stuff then use beverage cartons. Use cartons if you aren't sure, maybe.