serious games vs enertaining games

So there are many similarities between serious and entertainment games, in fact I think that the line between them is almost non-existent sometimes. Now, to compare and contrast the two we need to find some factor or factors that can be used to separate the two, so one good defining thing in a serious game is whether or not it is simulating realistic problems to deal with, for example in Simcity you build a city and run it, the profit vs expenses is a very realistic problem to deal with  there are actually a lot of good examples of realistic problems in Simcity meaning it could be viewed as a serious game. Now can a serious game be entertaining?  The answer is yes, an example of this is a built-in sandbox mode which a lot of strategy or simulation games have. Sandbox mode is where you have unlimited resources to build with/use.So Overall I think that the differences are so minimal that there's really no point in categorizing them separately.  I mean By definition a game is something that you play for fun if it teaches you something that's an added bonus.