Cornstarch works pretty well as a baking ingredient and a general-purpose thickener, but not everybody likes to use it. Corn allergies aren't uncommon, for one thing, and some cooks have dietary restrictions that rule out grains or grain-based products in general. Tapioca is a useful cornstarch substitute in those scenarios.
A Starch Thickeners Primer
You've probably used flour to thicken a gravy at some point, and it works well enough. It gives a finished sauce a matte, opaque appearance, and you'll need to use a relatively large quantity and cook it for a long time because wheat flour isn't a purified starch, but it works.
For a lighter sauce that's glossier, lighter and thickens quickly, you'll usually opt for cornstarch instead. Cornstarch is a purified starch, so it thickens more quickly than flour and at a lower temperature. It gives the sauce a nice glossy, translucent finish.
If you are looking for a cornstarch substitute, tapioca starch, arrowroot and potato starch are all good options. Tapioca starch is often the easiest to find.
Corn Starch vs. Tapioca Starch
The two starches are very similar in many ways. Both are highly refined, pure starch powders. Both thicken quickly, and both give a glossy finish to sauces and fillings.
There are differences, though. The first and most obvious is their respective sources. Cornstarch is made from corn, while tapioca is refined from cassava roots. This doesn't matter much culinarily since both thicken in much the same way. Cornstarch is a slightly stronger thickener, which won't matter much in small quantities but becomes important as you scale up your recipes. Bob's Red Mill, a big player in the gluten-free market, suggests using 4 tablespoons of tapioca starch to replace 3 tablespoons of cornstarch.
Some nonculinary factors may influence your choice of starch as well. Since corn is a grain, anyone who is avoiding grains for dietary reasons might prefer tapioca. Most corn is also genetically modified, so anyone who avoids GMOs might favor tapioca for that reason since cassava is not genetically modified. Finally, of course, anyone with a corn allergy should opt for a cornstarch alternative.
Tapioca as a Cornstarch Replacement
Tapioca can be used in most recipes that call for cornstarch, but there are some minor differences. Tapioca thickens at a slightly lower temperature, but it also loses its thickening power at a lower temperature and after a relatively short time. It's best not to add it to a sauce that will boil or simmer for a long time until you're almost ready to serve.
On the other hand, cornstarch doesn't handle freezing and thawing very well. This makes tapioca the better option for things like pie and pastry fillings that will be frozen. Tapioca also works better in a lot of gluten-free recipes, where it helps with browning and crust formation and gives your baked goods a more pleasant chew than other starches.
Explore Your Options
If you're trying to get away from using corn, or if you're experimenting with gluten-free baking, it's worth keeping a handful of alternative starches in your pantry and testing which ones you like for which purposes. They'll all work well as thickeners – for example, arrowroot is a cornstarch substitute, potato starch is an arrowroot substitute and so on – but they all have their distinctive characteristics, and you'll eventually find reasons to favor one over the other in a given recipe.