What is the difference between surface plasmon and surface plasmon polariton? I'm trying to understand this reading article linked below and I still don't know how to explain this simply, without need to derive everything mathematically. Can someone just write here how do SP's and SPP's differ?
http://dipc.ehu.es/etxenike/admin/documentos/archivos/publicaciones/307RPP2007.pdf
Moreover while reading this article : http://daedalus.caltech.edu/publication/pdf/0801_opinion.pdf I think that they are writing about SPP's despite of using SP term.
So maybe there's no difference at all?
 A: If you had a neutral plasma (which can be the free charges in a metal) and you pulled the negative and positive charges apart and let them go, they would oscillate due to the electrostatic potential. This is an excitation known as a plasma oscillation.
A Plasmon is the quasiparticle associated with plasma oscillations (analogous to phonons being the quasiparticles associated with mechanical vibrational modes).
Surface plasmons (SPs) are plasmon excitations at the boundary of the material.
Polaritons are quasiparticles that exist when an EM mode is strongly coupled to some other type of mode, i.e. if you have light strongly coupled to some other physical excitation then the particle picture is inaccurate if you treat the 2 degrees of freedom separately (b/c particle number is not conserved). So instead of saying you have some photons and you have some particles representing the excitation, instead you have a hybrid particle that is simply called a polariton. Because there are lots of types of excitations, such particles are called _ polaritons, where _ is the name of the particles of the excitation.
Therefore Surface plasmon polaritons (SPPs) are the quasiparticles of the coupled modes of an EM field and a surface plasma oscillation. Although surface plasmons are not the same as surface plasmon polaritons, from the context the two are rarely confused. In addition the charge oscillations will create an EM field, and so you can't create an SP without it automatically being part of an SPP. And since "surface plasmon polaritons" is a mouthful people often use the term SP even when they are referring to the entire excitation itself and therefore they technically mean SPP. 
A: There's no difference between plasmon and plasmon polariton. Both of them indicate the resonant excitations involving electromagnetic wave and collective electronic motions simultaneously. 
"surface" stresses that the excitation in many cases occurs at the interface of a metal and a dielectric. However, there exist bulk plasmons as well. So "surface plalsmon" and "plasmon" don't necessarily mean the same thing. 
Besides, you will see key word "localized" with "surface plasmon". That's because surface plasmon could exist on an extend surface or the surface of a finite nanostructure, e.g., a nanoparticle. The former is usually mentioned as just "surface plasmon", the latter "localized surface plasmon". 
Reply to your follow-up question: 
As for the conceptual difference between surface plasmon and surface plasmon polariton, I think Punk_Physicist has well explained it. The polariton here means the mixture of both electronic and electromagnetic excitations. In fact, these two are always happening together. Section 1.1.2 in the paper you gave tries to put forward a theoretical formulation for surface plasmon, so to say, electronic excitation alone. They let light speed be infinite while keeping frequency finite, then everything becomes electrostatic. You can see they use electric potential, which indicates electrostatic studies. Under these (unrealistic) assumptions, electronic excitation, surface plasmon here, is obtained without electromagnetic wave (clearly because it is electrostatic). 
