Meaning/picture of the statement: "Turbulent flow is chaotic. However, not all chaotic flows are turbulent" Wikipedia states that 

Turbulent flow is chaotic. However, not all chaotic flows are turbulent.

Someone give a picture for that?
 A: It's largely a matter of definition.  Here are some quotes.
From Springer Reference:

Definition There is no universally recognized definition of chaotic
  flows. Flows with properties that are neither constant in time nor
  presenting any regular periodicity are normally referred as chaotic.
  Fluid turbulence is generally found to be chaotic. It is also random,
  dissipative, and multiple scaled in time and space. It is a complex
  system of infinite degrees of freedom.

A paper full of state diagrams (but rather heavy on the math) for transitions to chaotic flow:  https://tspace.library.utoronto.ca/bitstream/1807/25484/1/Transition%20to%20chaos%20in%20converging-diverging%20channel%20flows.pdf 
And finally, a nice discussion at quora.com  (registration apparently required)

As Piyush Grover pointed out, a chaotic flow has to have mixing by
  definition. The  following answer assumes 'chaotic' to mean 'random'
  which is technically  incorrect. But I've decided to leave it here
  anyway, because I  think that's what the OP meant. However, I still
  think that you won't observe a k^(-5/3) spectrum in the case of
  chaotic advection.
I'm also adding Piyush's comment as a part of this answer.
Chaotic  but non-turbulent flows can have exponential mixing. There is
  a whole  field of chaotic advection based on this fact. In fact, you
  can have  exponential mixing of mass in Stokes flow, which is as far
  away from  turbulence as possible. This is often used to mix fluid
  efficiently at  micro devices (low Re), where turbulence is simply not
  feasible due to  energy considerations.
A  chaotic flow is one in which there seems to be a high irregularity
  in the behavior of one/all flow variables with time/space. While a
  turbulent flow certainly exhibits this behavior, there are also other
  properties that should be present for a flow to be called turbulent,
  one of which is high levels of mixing, i.e., mass/momentum/heat
  transfer.
This is a distinct (and perhaps the most useful) property of turbulent
  flows which is frequently exploited. When you try to mix the sugar in
  a cup of coffee by stirring it, you're essentially making use of this
  property. This effect can be clearly seen by looking at the velocity
  profiles of laminar and turbulent flows through a pipe. 

(Taken from Page on Flowcontrolnetwork)
The lines show the magnitude of horizontal/streamwise velocities with
  respect to height along a pipe. You can see that the turbulent flow
  has a much flatter velocity profile than a laminar flow, i.e., there
  are higher velocities close to the wall for a turbulent flow compared
  to a laminar flow, while there are lower velocities close to the
  centerline for a turbulent flow compared to a laminar flow. This shows
  that velocity (momentum for an incompressible/constant density flow)
  is transferred to a greater extent from the fluid elements close to
  the centerline to the fluid elements close to the walls in case of a
  turbulent flow.
A good example of a flow which is chaotic but is not turbulent is the
  trail behind an aircraft. Though the flow inside the jet trail is
  highly chaotic, it is not turbulent because it maintains the shape
  (diameter) for very large distances behind the aircraft, which means
  that there is very low/negligible mixing with the surrounding
  atmosphere.

