"White wheat" vs "wheat malt" vs "flaked wheat"?

White wheat and flaked wheat are both adjuncts and should be used in conjunction with a base malt (like wheat malt). From John Palmer's book on the former two adjuncts:

Unmalted wheat is a common ingredient in wheat beers, including: American Wheat, Bavarian Weisse, and is essential to Belgian Lambic and Wit. It adds starch haze and high levels of protein. Flaked wheat adds more wheat flavor "sharpness" than malted wheat. Use 0.5-2 lb. per 5 gal batch. Must be mashed with base malt.

From the same book on wheat malt:

Wheat has been used for brewing beer nearly as long as barley and has equal diastatic power. Malted wheat is used for 5-70% of the mash depending on the style. Wheat has no outer husk and therefore has fewer tannins than barley. It is generally smaller than barley and contributes more protein to the beer, aiding in head retention. But it is much stickier than barley due to the higher protein content and may cause lautering problems if not given a "Protein Rest" during the mash.

EDIT: As per Denny's comment, unmalted wheat like flaked wheat (and torrified wheat, among others) require a base malt in order to convert the proteins and starches in the wheat to fermentable sugars. If you ferment only with unmalted wheats, you will simply end up with a wheatmeal sticky mess that won't lauter very well, and won't have any sugars for fermentation. By adding a base malt rich with enzymes (as most are), those enzymes will help break down the wheat into fermentable sugars. This is what diastatic power is, the grain's ability to break down it's starches into fermentable sugars during mashing. Since unmalted wheat has no diastatic power, yet it does have fermentable potential, it has to rely on another (base) grain's diastatic power to hold the unmalted wheat's hand as they cross the road to fermentable-wort-street (so to speak).

Flaked wheat is raw wheat - it's not been malted. This means that the enzymes that would normally help convert the starches to sugars have not even been created yet, since this is one affect of malting.

"Normal" wheat is also called "red" wheat, due to the slight reddish hue it has. The grain is malted, and so has the ability to convert it's own starches in a mash.

White wheat, also malted, is a different variety of wheat that doesn't have the the genes that cause the red color. It typically has more proteins than red wheat, and also a slightly higher extract yield. So, it's often used in wheat beers where more haze from protein is desired.

All wheats will gum up a mash and make lautering harder if used in large quantities (>40%). Then rice hulls are recommended. 1lb/0.5kg per 5 gallon/20l batch.