Malted wheat, as the name suggests, is a fully modified, malted grain. Flaked wheat is not malted, therefore requires extra effort to extract it's potential sugar content, which will be lower than malted wheat. Flaked wheat is traditional in Belgian witbier and lambics, it contains more starch and higher levels of protein than malted wheat. It adds more mouthfeel than malted wheat and has a different taste, which is noticeable when used in larger quantities. If the grain bill consists of more than 25% flaked wheat you should consider a cereal mash, or precooking the wheat in order to gelatinize it so you can extract more sugars out of it. The addion of 6-row can aid conversion since the barley contains a higher percentage of enzymes than 2-row.
Torrified wheat is unmalted wheat that has been heated very quickly to get the kernel to puff up, kind of like popcorn. Torrified wheat adds a different flavor to the beer and the grain is gelatinized so you don't have to cook it. I have not used this grain so I don't have any experience with it. However, I have used malted and flaked wheat, I use flaked in smaller percentages for body, complexity and a starch (lambics need starch). I use malted for wheat beers in percentages of up to 70% of the grain bill, it tastes lighter, more delicate and less "grainy" than unmalted, plus it doesn't make the beer very heavy on the body.