In my experience,
Luc and Soph are the kind of shortenings that are only used to grab someone's attention ("Hey Soph, could you hand me that pencil?").
For me the difference between casual shortenings like Soph and nicknames like
Sophie are whether the bearer would ever introduce themselves with the name. So it would be perfectly normal for a
Sophia to say "Hi, I'm
Sophie," but rather unusual for a
Sophia to say "Hi, I'm Soph".