Dry Ice and Liquid Nitrogen all fall under the "Extreme and Sub-Zero Cooling" Category along with Phase, SS, Cascades, etc.
I refer to Dry Ice as "DICE" (D-ICE = Dry-ICE). Liquid Nitrogen I refer to as "LN2" (Liquid N2 = Liquid Nitrogen (N2)).
If you want to avoid using "pot" to explain how it works, use synonyms such as: container, basin, bowl, bucket, can, canister, crock, crucible, cup, jar, jug, kettle, mug, pan, pitcher, receptacle, saucepan, tankard, urn, vessel.
I like to call mine a Pitcher of DICE