Fanfic = fiction written in an established “world” by fans of said world. Usually found on the internet these days, usually terrible.
Twilight fanfic = fanfic in the Twilight world.
50 Shades started as fanfic put on Twilight fan sites. It got really popular, extremely popular. Popular enough that publishers approached the author about actually publishing it. So she “scraped off the serial numbers” (changed character names, removed references to the larger copy-written Twilight world) and walla, an incredibly poorly written financial juggernaut was born.
And you should know about it only if you want to actually know what you’re talking about when slamming 50 Shades. If you’re comfortable only knowing it’s awful then that OK too.
They do look at that sort of thing, I was getting chased around by some Canadian publisher but I didn’t have the time or inclination.