Yeah I am English. I would never call a cake tin a cake pan. Same with a roasting tray is never called a roasting pan. For it to be a pan it has to go on a hob. Even the way you describe things like a sauce pan seems contradictory, by your definition it should be a pot rather than a pan. It’s interesting to note what local differences exist in the use of language.

You definitely can do high heat cooking in a pot. Most of them are stainless steel or cast iron after all, the material doesn’t care.

Edit: forgot to mention that you can also have oven trays, which are flatter than a roasting tray. Roasting tray would be for say roasting potatoes or meat with sauce, and a tray would be for pizza or flatbread or chips.