The difference between healthy remorse and shame is that remorse says, "I did something bad", while shame says, "I am bad". Remorse focuses on a behavior, while shame focuses on the self. Remorse makes you concerned about the feelings of others, while shame makes you only concerned with your own feelings of worthlessness. Shame does not motivate change because it leads to hopelessness. If I believe that I am bad, I will feel powerless to improve things. Thus, shame is highly correlated with things like addiction, depression, violence, and aggression. Shame will make you want to run away from the problem, while remorse will motivate you to fix it.
Spiritually, shame is very dangerous because it makes you want to hide from Allah, rather than seek forgiveness and try again.