Dessert is dessert wherever you are: something sweet that you eat after your main course. Breakfast does not get dessert, but my children still ask for it. Lunch should not get dessert but sometimes it does. Dinner, conversely, doesn't always get dessert around here. Sometimes your chewy vitamin is dessert. You takes what you gets. If I was a good French mother, dessert would always be fruit. I'm neither good nor French.
I digress; dessert is easy, is my point - so long as you're talking semantics rather than parenting.
Pudding is another matter entirely.
In Ireland (and the UK, I daresay), pudding mostly is a synonym for dessert. Thus: "What's for pudding?", "Where's my pudding?", and "I want pudding!"
However, it does have a couple of other specific uses:
steamed pudding - a dessert traditionally made with suet (animal shortening, like Crisco) that comes out cake-like but is eaten hot. It's a more old-fashioned thing, and most people these days only encounter one at Christmas - Christmas pudding is a dense, dark, alcohol-soused mixture of raisins, sultanas, currants, mixed peel (and glace cherries if you're into that sort of thing), just about held together by some fluffy stuff. It's basically just another form of Christmas cake, but to be eaten warm with whipped cream and brandy butter. Variants might have amusing names like "spotted dick" or "pig's bum", as well as the more palatable-sounding treacle pudding.
blood pudding - in Ireland this is black or white pudding - definitely a savoury, not a dessert. It's a sausage made with pigs' blood that you might fry up a few coins of for breakfast with your rashers and egg. You either love it or hate it.
In the US, pudding is a specific type of dessert - a thick, viscous, sweet slurpy stuff that's often vanilla or chocolate flavoured. The closest thing to it I might have encountered in Ireland is Angel Delight. Something between the texture of thick custard and slightly runny blancmange, maybe. You can mix it up from powder or buy it ready made in little individual pots, or probably even make it from scratch.
So we have learned that pudding is always dessert (except when it's not) and dessert is not always pudding. Did I clear everything right up? Oh good.