I am having difficulty understanding the concepts of phase space, state space and phase portraits.

From what I've seen, a phase space is a vector field representing the behavior of points in a dynamical system.

A phase portrait is a set of curves in a phase space corresponding with a given initial condition.

I'm not sure what a state space is but it seems similar, if not the same, to phase space.

An example is given that . And I am given this graph corresponding to this equation.

Would this be a graph of the phase space? What would the phase portrait look like then? I'm pretty lost on how to construct a phase space/ phase portrait.

Thank you.