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Warrigal comments on What are your rules of thumb? - Less Wrong
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What's the difference between a boundary case and an extreme case?
Example: testing a multiplayer game. Boundary cases: a game running with no players / max players. Extreme case: game running with a lot of lag and interference.
Generalizing this to: boundary cases lie on some kind of natural boundary. Extreme cases are for things that don't have boundaries (e.g. you can always have more lag).
Also boundary cases aren't necessarily extreme, e.g., if you have some kind of optimizing buffer that kicks in when there are at least 10 players, 9 player and 10 players (and going from 9 to 10 and conversely) are boundary cases but not extreme cases.
I don't think there is one. At least not mathematically, which is where I do all these checks anyway. Solving PDEs ho!