https://www.reddit.com/r/AskBaking/comments/1ec28vj/frozen_dessert_vs_ice_cream/

from the first response...

It's about fat content and how much air is in it.

There has to be a minimum amount of fat to be labelled "cream" and overrun, or how much air is whipped in, has to be under a certain amount too.

So "frozen dessert" can range from anything like premium high quality plant-based ice cream to cheap airy whipped coffee creamer that is mostly air like a tub of Cool Whip. "Frozen dairy dessert" is emphasizing that even though it is not "ice cream" it is entirely milk based, probably low fat.

There may be a rule of thumb out there but there is so much variation brand to brand and even product to product that there is no hard and fast rule. The main thing is work quickly with cold tools and you will retain a pleasant texture when refrozen.

The FDA requires that ice creams with solid additions (nuts, chocolate, fruit, etc.) contain at least 8 percent milk fat, while plain ice creams are required to have at least 10 percent milk fat.

Labels like "ice cream" "premium ice cream" and "super premium ice cream" are regulated terms and refer to how much of the final product is air but I don't know the percentages.