Durability refers to the idea that your data will still be retrievable (ie no corruption) similar to S3's claim of eleven 9s of durability.
Reliability however would be say; the actual availability of the Web UI or API server that you download your data through. If it were down, that wouldn't impact the actual integrity of the data itself.
For anyone interested, any more than about five 9s of reliability is basically impossible anyway when it comes to human intervention. As an example, 6 nines of reliability would allow you 3 seconds of unavailability a year so 250 milliseconds of unavailability a month.
From a users point of view, being "unavailable" includes everything from going through a tunnel and having your mobile connection drop out to a shark biting one of the undersea cables in the middle of the ocean.
As you might imagine, with a human involved, they couldn't even get acknowledge an alert fast enough to meet that deadline let alone actually going about doing any repairs and diagnosis :)
It could be spread over multiple instances and redundant hardware as well but as with any system being touched by humans, it's near guaranteed that something will go wrong eventually.