How to distinguish the two? If the house wants you to lose and they want to win then you are facing a house edge, but if the house does not care about whether you win or lose then they are just charging you a fee
In fact, the house does actually care, and it wants you, and every other player for that matter, to win as the longer you play, the more fees they will collect. They are not interested in either you losing or losing you (whatever comes, or doesn't come, first). It is just the essence of the game, a zero-sum game, that you win and then someone else necessarily has to lose, or vice versa. It is the same with trading as exchanges in general are interested in you earning dough as the more you earn, the longer you stay in the game (pardon the pun)
Really simple, isn't it?