What is the difference between landing weight and end-of-mission weight?
End-of-mission is a time- (and case) dependent term. Your mission could end under a variety of circumstances. If your mission is to carry passengers from point A to point B and you have an uneventful flight, then end-of-mission and landing are the same thing. But (as stated above) if you have an emergency at some point, you might need to abort the mission. If this happens, then you are likely to end-up dumping as much fuel as necessary to get to your landing weight, because said end-of mission weight and landing weight will not be the same. 

Here is an oversimplified example:
Aircraft AC has MTOW of 100,000 kg and a MLW of 50,000 kg. The same aircraft has to get from point A to point B, without releasing cargo or ordnance. During the mission AC burns 100 kg of fuel per minute. Ten minutes after departure the pilot realizes that he has forgotten his watch and needs to land immediately. Now after 10 min flight AC weighs 99,000 kg. Since the mission is about to end before MLW is reached (99,000 ~= 50,000), the captain can either dump some fuel or circle around until AC's weight is at most equal to MLW.