Named in honour of the Federal Express company the FedEx Quest involves the PCs being retained to deliver something - possibly the macguffin - to someone. Traditionally the first addressee isn't at home, refuses to accept delivery or can't deal with whatever it is and sends them on. Sometimes for years. Arguably a simple delivery quest can be a FedEx as well if the delivery route is suitably annoying.
The PCs can also find the FedEx quest changing into something else if they end up having to use the Macguffin before it ends - or can be used to foreshadow as they are later sent to get back the Macguffin that they delivered in their first adventure … only to discover that the guy who ended up with it FedEx'ed it off with someone else, who may or may not have got lost on route.
The delivery can be anything from a magical ring containing the life force of an ancient uber-lich that needs dropping into a volcano, through a cartload of iron rations to a kid sidekick who needs to be delivered to his next of kin.
If the PCs just need to go and get something it's a Fetch Quest instead, even if they need to deliver it to someone other than the quest giver - the FedEx quest relies on the process of delivering the Macguffin.