Greeting, all.

I am posting this, after having read the above post.

The saying 'Hate the sin, but love the sinner' is quite commonly used in Christianity, but I must admit that I was slightly surprised to read it in an Islamic context.

From a Christian perspective I interpret the saying to mean the following:

• To be forgiving towards those who wrong me
• To be aware that we are all sinners, therefore I am not better than the next person - in comparison to God we all fall short!
• To never give up on people who are engaged in 'sinful' behaviours, to continue walking with them, talking with them, praying for them (as others do for me)

Would that interpretation be acceptable in Islam?

The reason I am asking is that it doesn't seem to add up, when I hear about Islamic rulings which call for the stoning of adulterous women, and the hanging of men who are actively gay.
Killing people seems in direct contrast to loving them.

The only way it would make sense was if the killing of the sinful person was actually seen as an act of love towards them ...
Is that the case?
Can somebody help me understand this?