What is the difference between Endurance Testing and Failover Testing?

Endurance and Failover testing have very different goals.

Endurance testing is a baseline application load that is applied over a much longer duration (normally at least 5-6 hours) that a standard performance test and is used to find things such as memory / CPU leaks ,threading problems (deadlocks, memory corruption), etc., whereas failover testing is when I apply a load to a system with multiple, redundant servers and arrange for communication to be cut off to one or more environment components to ensure that the remaining load is applied to the running servers. 

I am putting this in short as,
I like to thing of endurance testing as characterizing how long a system can continue to run before a failure whereas failover testing characterizes a system's overall ability to maintain it's operational function. So, endurance testing helps characterize reliability of a system and failover testing helps characterize availability of a system.