When we talk about $X$ being a RV with an exponential distribution $$f(x)= 1-e^{-\theta x} \,\,\,\,\, \text{for}\,\,\,\ \theta>0$$ we say that it describes the time between two events in a Poisson Process, where $\theta$ is the rate.
Does $X$ describe the time interval between two specific events? Or does it consider the time interval between any two events. So like if I have 3 events, does it consider the time interval between 1 and 2 and then between 2 and 3?
If the rate is constant, then does it mean that we actually know WHEN the event is going to happen? I don't understand how it can be random with a constant rate. If I have a machines that builds cars at a constant rate $\lambda$, then of course after a time $t$ I will have $t\cdot \lambda$.