FedEx considers Saturday a standard delivery day. As such, the private delivery service company makes both deliveries and shipments on that day. For example, if a sender chooses FedEx Home Delivery for a package that other delivery service companies schedule for a Monday delivery, then the receiver could conceivably get it on Saturday instead.
FedEx has a service option called FedEx Date Certain Home Delivery that allows senders to specify a delivery day, which may include Saturday. Other options available for when a person needs a package shipped or delivered at a certain time are FedEx First Overnight, FedEx Priority Overnight and FedEx 2Day services.