Is SlimROMS one thing or many?
I think I found my answer after a bit more search. 

I don't know why they use 's' and calls it SLIMROMs but Slim + Jelly Bean = SlimBean, Slim + Kitkat = SlimKat and Slim + Lollipop (LP) = SlimLP. 

SlimSaber on the other hand is an unofficial build of SlimLP. I suppose 'Saber' comes from custom toolchain Sabermod.