I don’t think there is any difference.

They’re both thickening agents. One is made from corn and the other is made from wheat. The corn one is obviously great for those who are gluten intolerant

Wheat free cornflour is usually a bit finer than the wheaten one and dissolves a bit easier when making sauces, custards etc. The wheaten one has the addition of wheat and is no good for people requiring a gluten free diet. I have used both before. They are pretty much interchangeable in recipes depending on your requirements and how much you want to spend. The wheaten one is cheaper than pure cornflour. They have a slightly different taste also.

I often use a Mouths of Mums recipe for Salt & Pepper Prawns. I have found that wheaten cornflour works a treat, but the corn cornflour doesn’t. Why would this be?

Pretty sure they can be used interchangeably, just use pure corn cornflour for gluten free.

Corn cornflour is gluten free so this is what we use in my household of coeliacs

The wheaten cornflour is cheaper but it has wheat in it. Some people are allergic to wheat. Others have coelic Disease which means they have intestine damage and can’t eat wheat, barley rye. Some can’t eat oats either as it has a protein very similar to the one in wheat..

As far as I know they work and taste basically the same. My best friend is GF so I only keep the corn one so that there are no mistakes if I am cooking for her.
I think the wheaten cornflower is often cheaper. I have found that the wheaten cornflower con sometimes leave a floury taste if it is not cooked out properly where the corn cornflower doesn’t seem to do it as badly but that could be my imagination.