It looks like most of the sibling responses view "pan" as mainly referring to a "frying pan", there is also a "sauce pan" that is likely what you are referring to.

Rough disambiguation: Frying pan - shallow with single long handle Sauce pan - deeper with single handle Pot - deeper with two loop handles

US resident here. To me, a "pan" is usually a shallow cooking container usually for frying/sauteeing. Not something you would boil pasta in for instance. For pasta/beans/soup i eould use a "pot."

A pot is used for boiling water, or cooking stews and soups. They typically have two small handles on each side.

A pan has short, usually curved sides, and is suitable for simmering small amounts of liquid, searing or frying. It will almost always have a single long handle.

Woks are the exception- the look halfway in-between a pot and a pan, though the design is more geared towards the same uses you would use a pan for. Although there are two small handled varieties, the thinness of the metal makes it much less effective at stews and soups because it doesn't hold heat well.

Saucepans are somewhere in the middle.

"Saucepans are round, vertical-walled vessels used for simmering or boiling. Saucepans generally have one long handle. Larger pans of similar shape with two ear handles are sometimes called "sauce-pots" or "soup pots" (3–12 litres)." [1]

[1] https://en.wikipedia.org/wiki/Cookware_and_bakeware

In the US, a "saucepan" is still usually considered a small pot. Only cooking nerds even know what a saucepan is.

In my eyes (I live in the US) “boiling” seems to only refer to boiling something in a pot. Like boil a pot of water (cause it to reach boiling point and bubble) then put in noodles.

Difference between saucepan and frying pan? Former you would use for boiling, latter, not so much...

A Pot. Pots are tall and are used for boiling, pans are low and used for sauteing.