There are different forms of starch to choose from for thickening sauces, each with its own strengths and weaknesses. Grain starches contain a high proportion of moderately long amylose molecules, and they make sauces that thicken quickly and congeal when cooled. The starch granules of grain starches contain small but significant amounts of lipids and proteins, and this makes grain starches to thicken at a higher temperature, and an opaque appearance hot or cold. Sauces thickened with grain starches are thick enough to slice with a knife (perfect for use in a pie filling), however, they become spongy and leak watery fluid when frozen and thawed.
Root and tuber starches contain less amylose, but their amylose chains are much longer than grain amylose. So you need less potato starch than you would wheat flour to thicken the sauce to the same effect (see table T07-5-1). Root and tuber starches granules contain much less lipids and proteins as compared to grain starches, so they thicken at lower temperatures, and have a translucent, glossy appearance hot or cold. However, the swollen starch granules are fragile and readily fragment into finer particles, so sauces thickened with root and tuber starches are thickest at their gelatinization temperature, and thin a little when cooled or reheated. These starches produce sauces with a clear and glossy coating (perfect for stir-fry), and they freeze and thaw nicely without change. Since acids encourage the fragmentation of starch chains to shorter lengths and lowers the gelatinization temperature, root starches are also affected by moderate acidity typical of yogurt and fruits, while grain starches can withstand the acidity better.