In the UK you will find cornstarch labelled as cornflour.
There is "self raising flour", which is white flour with the raising agent already added, great for when you are making sponge cakes.
"Plain flour" is what I would call ordinary US flour, no raising agent added and, for example, used for making a pie crust.
Then there are bread flours, wholewheat flours, potato flour, in fact you should be able to find every kind of flour you need.