Slackware uses the sysvinit program, but doesn’t have System V-style scripts. Which is somewhat confusing, but sysvinit is a basic init program that will just do whatever /etc/inittab tells it, so you can write your startup scripts to work however you want.
Slackware uses what people tend to call a BSD-style init, but it’s nothing like the modern BSDs, nor the older BSDs, not really. If you use Slackware, you’ll learn how Slackware’s init system works, but that’s about it.