In the definition for sensitivity to initial conditions what exactly does the distance between trajectories mean?

Question

I've seen this definition for sensitive dependance in Modeling Life (Garfinkel et al, 2010): $$d(M_{t} - N_{t}) = e^{\lambda * t} * d(M_0 - N_0)$$ or alternatively from Wikipedia: $$ {|\delta \mathbf {Z} (t)|\approx e^{\lambda t}|\delta \mathbf {Z} _{0}|}$$ with $\lambda$ being greater than $0$ indicating divergence of trajectories. I'm confused as to what exactly distance between trajectories means. The first definition to me implies the distance between two points in state space.
However since in a chaotic system the attractor is bounded, an arbitrarily large distance between two points cannot be possible, there exists an upper limit.
Then what does "distance between trajectories" mean?
I'm a biologist rather than a mathematician so be gentle with the answer ^^