Well, in that they have lots of other services, sure, but FedEx does have both long-distance (FedEx SameDay) and shorter-time-window local (FedEx SameDay City) same-day services.
The main difference would be that FedEx isn't subsidizing rates with investor money to fuel growth, so its more expensive.
Doesn't really matter, but you could see a need for an "equipment and stuff" on demand in an hour type of service catering to these events.
Similarly, every wedding venue can have an "emergency" service for missing stuff ("Florist flaked? We can put petals to the metal and have them there in an hour!")
These are perhaps more extreme, but I'm sure there are any number of restaurants in your area that don't deliver, but might like to have that capability. One morning last week I went to my local bagel shop to find the manager loading dozens of boxes of bagels into her car (catering for the local school's Teacher Appreciation Day). There is insufficient demand for the bagel shop to have a full time delivery driver, but big catering orders UberRush might really fill a need for them.
https://developer.uber.com/docs/rush
I'm curious how you might compare them to FedEx's docs?
As an example, the developer document solely for obtaining shipment rates is 98 pages long.
FedEx SameDay City Priority seems to guarantee delivery within 2 hours from package ready time within the shortest (0-15 mile) delivery range, and its available in a lot more cities than UberRUSH.