Causal relationships in the real world can have diverse mechanisms with differing statistical signatures. We investigate whether people can distinguish between causes that merely change the timing of events ('when' causes) and those that bring about or prevent those events ('whether' causes). We designed experiments where the rate of an event varies over time due to one such causal influence. Events were shown in real time in Experiment 1 and as a timeline visualization in Experiment 2. Our results suggest that people are capable of identifying 'when' and 'whether' causes but with a distinctive pattern of confusability: sometimes mistaking Generation with Hastening; Prevention with Delaying. We developed a Causal Abstraction from Summarizing Events (CASE) model, which effectively captures people's judgments. We discuss how this line of research can be extended to study human cognition about dynamic causal influences and its relevance to real-life judgment and decision-making.