dtgreene: I prefer to call those latter games diablo-likes, much like the term "roguelike" is used to refer to games that have many similarities with the original Rogue. 
 toxicTom: Makes sense, but so many people say ARPG and mean Diablo-like that it's probably better to check back what they mean.  
 As for Rogue-like... and Rogue-light and what not - seems this got a bit muddy too, with different people meaning different things and some very hard core and "trve" (and vocal) complaining the concept is watered down... 
 I draw the line between roguelikes and roguelites in that roguelikes must be strictly turn based the way Rogue was (enemies move only when you move, no real-time time limits (turn limits are OK)).  
 Interestingly enough, I do not consider permadeath (or even approximate permadeath, like in a game like Shiren the Wanderer) to be a necessary condition for a game to be a roguelike.  
 By the way, here is an interesting exercise regarding the genre definition: 
 Look at the Berlin interpretation of what a roguelike is. 
http://www.roguebasin.com/index.php?title=Berlin_Interpretation. (Yes, not everyone agress with this definition, but it will work fine for this exercise.) For each of the high value factors in the definition, ask yourself the following question: 
 * If a game strictly fit the definition of a roguelike, except for that particular factor, which it flagrantly violates it, is the game still a roguelike?  
 For me, the result is that "random environment generation" and "turn-based" are the only aspects that are strictly necessary; any other one could be omitted and I would still consider the game a roguelike.