Blackbody radiation Vs thermal radiation I am having problems connecting the following 3 concepts:


*

*Blackbody radiation and thermal radiation1.

*Optically thin and optically thick mediums.

*Local thermodynamic equilibrium (LTE) and thermodynamic equilibrium (TE).


I am trying  to work out how these are connected. e.g. if you have a optically thin medium in TE does it produce blackbody or thermal radiation. Given that I can't even seem to find clear definitions of each of these properties I am having no luck in this task. Thus my question is this: How are the properties in the list above linked? (definitions would also be helpful)
1for simplicity I am taking the term thermal radiation to exclude blackbody radiation. (non-standard) 
 A: Thermal radiation is the ever-present radiation that is produced inside material bodies and gets more intense with higher temperature; its frequency spectrum depends on the temperature and composition of the body. The body does not need to be in thermodynamic equilibrium, it suffices that its elements can be assigned local temperature. The spectrum often shows characteristic peaks and holes (liquids, solids) but universally drops to zero for zero and infinite frequency.
Black body radiation is thermal radiation of a hypothetical body that has everywhere the same temperature and is a perfect absorber. Of all bodies at the same temperature, it has the most intense thermal emission at any frequency. The spectrum is smooth, without any lines or peaks or holes, but it drops to zero for zero and infinite frequency as well.

if you have a optically thin medium in TE does it produce blackbody or thermal radiation

It produces thermal radiation that is characteristic of the medium; if it is optically thin, the net intensity per surface area will be lower than intensity from a body of the same composition but greater thickness.
A: BB Radiation is Temperature related and causes energy loss from the medium. Optical depth describes how much energy is absorbed by a medium when light is incident upon it. But examining these effects together with any other energy losses and gains you can determine if the system is changing temperature. If it is not it may be considered to be in LTE.
(Global Thermodynamic Equilibrium means no energy is moving in the entire system, it will be the final state of your system including the medium.) 
You want to dig out the equations too, I guess...
