Hard vs soft wheat? 

Hard wheat is usually higher in protein (>10%) than soft wheat (<10%). Their flours turn out different, which affects baking properties and such. Hard is better for pasta and bread, while soft is more delicate and better suited for pastries and cakes. 

Red vs white wheat?

Red wheat has a reddish bran, and white wheat has a white-ish bran. Ironically, most white flour is made out of red wheat where the bran is sifted out or bleached. 

Red wheats have a higher sprout resistance than white, meaning that they are less likely to sprout in the fields pre-maturely. Pre-harvest sprouting affects the flour negatively. 

Winter vs spring wheat? 

Winter wheats are sown in the fall and form strong root networks. They typically face less competition from weeds and have a higher yield than spring wheat. Wheat started out as a winter crop, and spring types only emerged with domestication in colder climates, where winters are too cold for the plants to survive.