Angel Food (or Devils Food) are not common cakes over here. Brownies are a (relatively) recent thing too. The most common cake is the Victoria Sandwich, or a sponge cake (which is similar but much lighter and has no fat in it). A chocolate cake/sponge is the same recipe as the others but you take out an ounce of flour and replace it with cocoa.
You have to grease your pans otherwise they stick to the sides of your cake tin (not pan!) because until relatively recently cake tins were make of steel not non stick. Even now, unless you spend ££ on non stick, its best not to bother and just buy stainless steel and line them with greaseproof paper (baking parchment I think in the US?).
Oh and we call it cake mix, not batter.
A lot of the recipes now in common use in the UK are a direct result of the war. When you didnt have much, you made it stretch so thats why a lot of our cake/biscuit recipes are less luxurious than the US versions.