“saved by love” and “choose recovery because loved” look similar on the surface, perhaps because the end results look similar, but they’re so different really. It’s passive vs. active; a story is about the person who’s making choices, being proactive. If Character A is saved by love, then it’s not them the story is about, it’s about their savior, Character B. If Character A chooses recovery, then they’re the one the story is about. Character B is the side character this time.

One is the narrative of taking what is broken and fixing it. It is not about the ‘broken’ person, it’s about the ‘savior’ who ‘fixes’ them.

One is a tale of healing. It is not about one person 'fixing’ the other, it’s about the person who makes a conscious decision to not let their pain define them.

In one, the story is about the person who loves the hurt person, and the hurt person’s pain is incidental to the main character’s arc. In the other, the story is about the hurt person themself, and the other person’s love is incidental to their arc. 

I hope I’ve said this well enough. My words may not be coming out the right way to express what I’m trying to say. Sometimes they do that.