The word “dessert” originates from the French word, “desservir”, meaning “to clear the table”. High end restaurants and hotels still use it to list sweet dishes, but more establishments use sweets, puddings, even afters these days.
You are quite right only2garners, in that countries like the US generally use the term desserts, but particularly the UK have adopted the wider range of meanings.
Personally, I’m happy with pudding.