Causal slippery slope is about causality. Think of it literally. If you kick that pebble it will hit that bigger rock below with enough force to move it, then that rock will hit a bigger one below, and so on, until we have an avalanche.

Slippery slope aside from that doesn't hinge on causality. "If we allow gays to marry, soon people will be marrying goats and even typewriters." The idea is that people will make judgments, decisions that up the ante, so to speak, but we're not saying that allowing gays to marry will "physically" cause people to marry goats, etc.