Trinity Burnt Creme is basically the same thing as creme brulee. It's a rich baked custard, served with a light crispy caramelized sugar top made possible by a broiler, gas torch, or in the old days a red hot iron.
There is also a Spanish version of the dessert called crema catalana. It differs in flavorings, staring cinnamon and citrus zest, which is much closer to the original published French versions. As far as I can tell, the current 'traditional' flavoring for creme brulee/burnt cream is vanilla.
The French get credit for having it in their cookbooks first. But the English try and weasel in because some of the French cookbooks called in creme anglaise (English Creme). Some heterodox historians consider Spain the country of origin. Sadly, they're all deluded, because as everyone knows, creme brulee was invented single handedly by Catherine de Medici when she left Italy to bring cuisine to the barbarians. :P
I've notice you included creme caramel in your list, which doesn't quite belong. It's a distant cousin of the brulee family. It's prepared by lining a mold with molten caramelized sugar, letting it solidify, filling it with custard base, and baking/steaming it done. You must let the cooked custard rest for at least a day, because the caramel steals water from the custard and dissolves, making a nice sauce. The dish is usually inverted and unmolded just prior to service.