Cordial obviously has a different meaning in the US. In UK & Ireland it refers to a fruit juice concentrate.
i think the closest description would be a digestif or a liqeuer?
My wife is partial to a Baileys, my father back in the day would be a Drambuie and my mother a Cointreau. I’d drink a Limoncello if offered (has anyone ever ordered and paid for Limoncello rather than given on the house?). But the only digestif I’d order would be a brandy or an armagnac.
i have a friend who loves Poire William.