Causal processes in the real world can have diverse effects. %operate through diverse mechanisms. Some generate or prevent events, while others just change the timing at which events occur. In this paper, we extend prior research on causal reasoning by showing that people's representations of causal influences include both existential (generating and preventing) causes and temporal (hastening and delaying) causes. We used a paradigm in which the rate of an effect event varies over time due to different types of causal influence. Across six experiments, we found that participants could recognize and distinguish between existential and temporal causal influences but had systematically non-uniform error patterns. Response patterns were influenced by both the display format (real-time experience vs. timeline summary) and the option format (causal verbs vs. causal descriptions). We examined why participants frequently labeled generating stimuli as hastening and preventing stimuli as delaying when they experienced event streams in real time, but not when reasoning about a timeline summary of the same events. We developed two process-level models to account for these patterns, showing real time causal inferences reflect fast perceptual processes, while timeline-based judgments reflect slower offline counterfactual reasoning.