# Formulation of State Space Models

I have seen the following formulation of state space models:

$$z_{t + 1} = A z_t + B u_t + \epsilon_t \\ y_t = C z_t + D u_t + \delta_t$$

But sometimes it is also written as follows: $$z_{t} = A z_{t-1} + B u_t + \epsilon_t \\ y_t = C z_t + D u_t + \delta_t$$ Why are there different formulations for computing the next state?

When to use which formulation?