@St1ka, @montyontherun: you're mostly right. it is a custard. What us Yanks call "pudding" is just a basic sweet custard. It isn't all chocolate (my favorite is a vanilla pudding with pearls of tapioca starch throughout. Kind of like boba tea meets custard and I love it)
I thought "flan" was a particular caramel baked custard thing, but I am seeing that the internet is proving that assumption somewhat wrong! We are all learning things today!