Electromagnetic wave reflection vs. light reflection Related: x-ray interaction with atmosphere
I know that electromagnetic waves of particular frequencies reflect from the ionosphere. And the light (which from one perspective is an electromagnetic wave) also reflects from the.. let's say snow. 
These types of reflection have the same nature or different mechanisms are involved here?
 A: Electromagnetic radiation will reflect from any change in refractive index.
For light reflecting off snow you have an air/ice boundary, and the refractive index of air is about 1.0 while ice is about 1.3, so you get reflection. Actually you get multiple reflections which is why you get a diffuse scattering and why ice looks white.
For RF waves reflecting off the ionosphere, the ionosphere refractive index is changed by the free elections in it, so there is a refractive index mismatch between the very low pressure air below the ionosphere and the ionosphere itself and this causes reflection. It's a bit hand-waving to claim it's just that the ionosphere has a different refractive index, but that's a good starting point. If you want to look in more detail see http://ecjones.org/physics.html and many other easily Googlable articles.
So I suppose the mechanisms are basically the same.
A: It was such a simple question, but you guys gave such complicated answers:(
It is really not that hard to answer: in both cases, we can model the reflection as light (an electromagnetic wave) passing through a medium with changing index of refraction. In both cases, we can analyze it as waves or rays, but it is better to analyze both as waves. In both cases, waves are reflected when the index of refraction changes (as Rennie already pointed out). In that sense, it is the same mechanism.
Now true, technically, what happens in the ionosphere is a bit more complicated, with radio waves being bent gradually back to earth rather than reflected at a sharply defined boundary with a discontinuity in index of refraction, but that is ignored when actual users of such radio communication (such as radio amateurs) work in terms of the (virtual) height of the relevant layer of the ionosphere (layers D through F2). See http://www.electronics-radio.com/articles/radio/basic_radio/propagation/ionospheric-hf-propagation.php for a simplified explanation of ionospheric reflection, http://www.qsl.net/zl1bpu/IONO/iono101.htm for more details.
Oh, there is one other aspect in which they are different: since ice and air are both dielectrics with ice having the higher index, the reflection is phase inverting. We don't usually care, because the phase is lost in the diffuse reflections anyway.
But since air in the ionosphere is conducting, we have to model it as a reflection where one medium is dielectric and the other conducting, so the treatment of phase is different. If it were a good conductor, the reflection would be phase preserving; but since the ionosphere is rather weakly conducting, the full electromagnetic wave treatment of this case is rather difficult, and is not found in elementary E&M texts: one has to resort to odd or old sources like Frankel to see it fully analyzed. Yet as the QSL site reference above mentions, one can at times hear the effects of phase distortion in HF signals reflected off the ionosphere. So the difference is relevant.
Come to think of it, my own answer turned out to be more complicated than I expected when staring it, too;) But I hope it has answered your question more fully.
A: First of all, in order to describe this kind of phenomenon the EM "perspective" is enough, but if you want to look at the interaction between light and one atom you need the description given by quantum electrodynamics. So light is not an EM wave from all perspectives!
The reflection due to the ionosphere and the one you observe with snow are the same and it is called diffusive reflection. Because snow and ionosphere are not ordered/regular medium in fact you observe a reflection in all directions. With a mirror, for which atoms are regularly spaced, reflection appears only in one direction which explain Snell-Descartes.
I hope my answer is clear!
A: I am here because of the bright spots on Ceres. It does not have the dense atmosphere of the Ionsphere, so I will quote you a reference on the phenomena of Reflection.
This is covered by Philip M. Morse "Chpt 7 Hndbk of Physics Vibrations of Elastic Bodies; Wave propagation in Elastic Solids Sec 4. Reflection from a Plane Interface, Surface Waves"
'(if the free surface were the surface of the earth, these would be SH waves) is reflected without change of type and with amplitude -1.  In other words P and SV waves interchange on reflection but SH waves remain SH waves.'
The terminology is on 3-99 he is using the physical analogy of Seismic waves.
Compressional waves, or longitudinal waves  = P
Shear or transverse                         = S
Shear Waves in a horizontal plane           = SH
The analogy is apt and he covers Rayleigh reflection and terms them "attenuated" not scattered.
In Part 6 Optics Sec. 6 Reflection and Refraction at a Plane Boundary
E. U. Condon of Colorado University 
Covers Snell's Law and Brewsters Angle.
Here the application of boundary conditions is tied back to Maxwell's Field equations
of Section 3 eqn. 1.17
Normal components of vectors  D and B
Tangential components of      E and H
**
