Not always and I'd suspect that being a "Full-Service Shopper" (vs "In-Store Shopper") pays better so a large percentage are likely both preparer and deliverer.
>>jiansh+(OP)
FSS are paid by the order–you see a preview of how much you'll make before accepting an order (broken down into IC pay, mileage pay, and customer tip). ISS are paid by the hour and sign on with an hourly wage agreement.
Haven't worked as an ISS, but I presume that they have no say in their orders as they aren't paid per order. I actually have no idea if they even get a portion of tips.