What is the difference between charge density wave (CDW) and charge ordering (CO)? I am suffering with the terminology of condensed matter physics.
When I read papers about strongly correlated electron system, sometimes I see the words "charge density wave" (CDW) and "charge ordering" (CO). They would indicate similar physical phenomenon, but I don't know whether I have to distinguish them or not.
Is there any difference between CDW and CO?
 A: Wikipedia has rather clear articles about both the Charge density wave and the Charge ordering (although without really establishing link between the two).
Clearly, the two phenomena may overlap, and some could even say that CDW is a particular case of CO or vice versa. There are however differences:
Charge density wave (CDW)

A charge density wave (CDW) is an ordered quantum fluid of electrons in a linear chain compound or layered crystal. The electrons within a CDW form a standing wave pattern and sometimes collectively carry an electric current. The electrons in such a CDW, like those in a superconductor, can flow through a linear chain compound en masse, in a highly correlated fashion. Unlike a superconductor, however, the electric CDW current often flows in a jerky fashion, much like water dripping from a faucet due to its electrostatic properties. In a CDW, the combined effects of pinning (due to impurities) and electrostatic interactions (due to the net electric charges of any CDW kinks) likely play critical roles in the CDW current's jerky behavior, as discussed in sections 4 & 5 below.

CDW are a state of a quantum liquid, they are necessarily a quantum phenomena and appear in, e.g., superconductors. From a theoretical point of view the important feature is that they can appear in 1D materials/linear chains (in which one cannot have a phase transition). CDW may have a period extending for many lattice sites. CDW can be dynamic and carry current.
Charge ordering (CO)

Charge ordering (CO) is a (first- or second-order) phase transition occurring mostly in strongly correlated materials such as transition metal oxides or organic conductors. Due to the strong interaction between electrons, charges are localized on different sites leading to a disproportionation and an ordered superlattice. It appears in different patterns ranging from vertical to horizontal stripes to a checkerboard–like pattern 1 , and it is not limited to the two-dimensional case. The charge order transition is accompanied by symmetry breaking and may lead to ferroelectricity. It is often found in close proximity to superconductivity and colossal magnetoresistance.

CO is inherently a phase transition, described by models that are similar to the Ising model. Thus, the focus here is not on quantum nature but on critical phenomena, which may be rather classical in nature (coherence length shorter than spacing between charges, the ordered-unordered transition is driven by temperature). The materials are metal oxides or organic conductors - that is bulk materials (while CDW is more common in composite materials, like linear chains or layered structures). Since CO is a phase of matter, the focus is on the properties of the phase transition, rather than on its dynamics.
