Does type of starch used for thickening make a difference in a fruit sauce?
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.