I get that you are laying down some technical language on us, but a tall pan is a pot in common English. Oil pans, bed pans, evaporating pans, gold pans, etc all use “pan” to describe that they are shallow vessels, significantly wider than tall. You can’t “pan for” a heavy particle in a “tall pan” because it’s not functionally a pan; a tall pan is a contradiction.

I would describe a sauce pan as a “culinary pan” but an actual pot, like how a tomato is a culinary vegetable but an actual fruit.