The majority of the flour we consume is made from a single species of wheat: Triticum aestivum, also called “bread wheat” or “common wheat”. It’s a species that’s been cultivated for hundreds of years, and like all crops that have been widely grown over long periods, different forms of it have evolved and/or been created over time. Nowadays we grow many different types of T. aestivum, all with different properties.
In America our most common wheats are Hard Red Spring Wheat, Hard Red Winter Wheat, Soft Red Wheat, Hard White Wheat and Soft White Wheat. These strains can be, and sometimes are, milled into what you might think of “single source” flours, but more typically they’re used in combination to make the flour products we find on grocery store shelves. Of the varieties, the hard wheats make up about three quarters of the annual harvest in the US, soft wheats about 20%, and oddballs like club wheat and durum (both of which are different species of wheat, and are used chiefly for cake flour and pasta flour respectively) make up the rest.
“Red” wheats are so named because of the reddish-brown color of the bran that surrounds the endosperm and germ. “White” wheats, by comparison, have a pale tan seed coat (and since they don’t require the same bleaching as red wheats, are typically more expensive). “Spring” wheats are so named because they’re planted in the spring and harvested in the fall. “Winter” wheats because they are planted in the late fall and harvested in the summer.
Is spring or fall wheat better for baking? Here there’s quite a bit of argument. All I can say is that historically, hard winter wheats have been more highly valued for bread baking than hard spring wheats. The reason is thought to be because, while spring wheats have more gluten, winter wheats have a higher gluten quality. I personally cannot vouch for the truth of that claim, and it may just be marketing. There are all sorts of interesting wheat products out there these days, so if you’re really interested in this topic, there is much to investigate.