Honestly saying, I don't even know the exact meteorological and physical difference between the said phenomena. If there are some books or papers regarding this or based on the fundamentals of radiation budget calculations please send to me.
You honestly confess to know little about the process, but at the same time you are using precise terms, and that is the best premise to focus the answer.
That, said, yes, there is a big difference between "surface net solar" and "surface net thermal" radiation. Solar radiation includes a wide spectrum of wavelenghts (actually the Sun is "almost" a black body), but, due to the high temperature of its surface (slightly below 6000 K -see the Planck "law" for the reasons...-), "most" of the radiation emitted is in the "shortwave", which is a generic term, but very common and meaningful in this context. Radiation emitted from the land surface and from the column of atmosphere sitting above it, is in a very different range of wavelenghts: in the "longwave" (IR). Again, this is related to the much lower temperature of this two "bodies" (say, on the broad average, around 285 K). Notably, there is a little overlap between the spectrum emitted by the Sun and the one emitted by the land.
Thus, when we reason on the balance "at the surface", you have two fluxes in each "band". The net solar radiation originates form a downwelling flux, coming from the Sun and penetrating the atmosphere, and an upwelling flux, that is composed by reflected photons (because of that, the net is *always* positive). For the longwave, you have again a downwelling flux, coming from all the layers of atmosphere above, and un upwelling flux emitted by the surface (land, vegetation, water...). As the temperature (and the emissivity) of the atmosphere is quite low (and always lower than the land surface), the downwelling flux is never greater that the upwelling, and therefore the net longwave (thermal) is always negative.
The sum of the net shortwave and net longwave is simply called "net radiation", which broadly represent the available energy at the surface.
Completing the Andrea's answer, you should see some books about energy balance and micrometeorological processes, like Oke (1988) - Boundary Layer Climates, Arya (2001) - An introduction about Micrometeorology and Stull (1988) - An introduction to Boundary Layer Meteorology.
It's discuss the role energy and radiation balance in differents areas.
Thank you very much Dr. Andrea. Your explanations are very useful. Could you please help me in finding relation between surface air temperature and one of the above quantities?
while your first question could receive a "simple" answer, this second is much more difficult! I support the advice by Marcos Vinicio. the book he mentioned is a very nice introductory book.
That said, we arrived to the concept of "available energy" at the surface. This energy (that is often a lot) must be conserved and can support a limited number of processes. It can enter the "body" (soil? water?) and heat it up. It can support the evaporation of water (a process that needs a lot of energy). Or, simply, this energy at the surface can be released as heat to the air.
This last "injection" of energy into the lower atmosphere produces an increase of its temperature. It is calle "sensible heat" just because you cal feel it! But, as you have probably already understood, there isnot (cannot be!) a simple relation between net radiation and air temperature, because not all of it will go into sensible heat. For instance, in an environment wher you have plenty of water, most of the available energy will be dissipated in water evaporaton, and air temperature will not change (this is call "latent" heat). In a desert, on the contrary, almost all of the available energy will be trasferred to the air, rising a lot its temperature.
This is the concept of "energy balance", which is -in princlple- a simple equation, but whose partitioning is a challenge in many fields.