Creating a recipe for a glazed fruit pie - what starch to use?
Use the tapioca starch, or, if you cannot find that, another tuber starch. It is more waxy than cornstarch, and therefore better suited for a glaze. It will give you a glossy, transparent appearance. 

Cornstarch is a mealy starch, with high amylopectin content, and creates a soft, fluffy, somewhat cloudy mass, not as glossy or as transparent as waxy starches. By the way, it shouldn't have an off-taste if you cook it through.  

I guess that most recipes haunting the Internet use cornstarch because it is so much more common in a home kitchen, and the home bakers found the result good enough for their purposes and/or were not aware that tapioca will give them a better end product. As you describe that you want a really good glaze, go for the tapioca.