Does type of starch used for thickening make a difference in a fruit sauce? I'm making fruit sauce to spoon, say, over a piece of cheese cake. American recipes typically call for corn starch to thicken it, but around here most people tend to have potato starch in their pantries. Does corn starch have any advantages over other thickeners for this particular use?
Per this page from  The Cook's Thesaurus  many starches can be used for thickening but some work better than others for certain applications. For the purpose of a fruit sauce arrowroot would probably be your best option.

arrowroot starch = arrowroot powder = arrowroot = arrowroot flour    This starch thickener has several advantages over cornstarch.  It has a more neutral flavor, so it's a good thickener for delicately flavored sauces.  It also works at a lower temperature, and tolerates acidic ingredients and prolonged cooking better.  And while sauces thickened with cornstarch turn into a spongy mess if they're frozen, those made with arrowroot can be frozen and thawed with impunity.   The downside is that arrowroot is pricier than cornstarch, and it's not a good thickener for dairy-based sauces, since it turns them slimy.
Arrowroot also imparts a shiny gloss to foods, and while it can make a dessert sauce glow spectacularly, it can make a meat sauce look eerie and fake.  To thicken with arrowroot, mix it with an equal amount of cold water, then whisk the slurry into a hot liquid for about 30 seconds.  Look for it in Asian markets and health food stores.   Equivalents:  One tablespoon thickens one cup of liquid.  Substitutes:   tapioca starch (very similar) OR Instant ClearJel®  OR cornstarch (Cornstarch doesn't impart as glossy a finish and can leave a starchy taste if undercooked.) OR kudzu powder OR potato starch OR rice starch OR flour (Flour makes an opaque sauce, imparts a floury taste, and can easily turn lumpy.  Use twice as much flour as arrowroot.)

The article lists each thickener with details on the best uses for each, downsides, and substitutions.