“Slippery slope” is about making an argument. “Domino effect” is about a chain of events.

Dictionary definitions are useful here. This is what the Collins Dictionary says: Domino effect: If one event causes another similar event, which in turn causes another event, and so on, you can refer to this as a domino effect. Slippery slope: If someone is on a slippery slope, they are involved in a course of action that is difficult to stop and that will eventually lead to failure or trouble. As you can see, the key difference is that in the domino effect, there is a 'chain reaction' of events where each event causes another one to happen. This is different from a slippery slope, which is a downward slide.

'A slippery slope' is used to describe a situation that goes from bad to worse and continues to get worse. 'A domino effect' is used to describe a situation where one event sets off a chain of similar events.