Photon and EM wave are the same thing. To say EM wave make photons is rather like saying H
2O makes water. Photon is a packet of EM wave energy. EM wave traveling is a bunch of photons traveling.
U Colorado has a decent presentation on it - any physics department lecture would do as they all study the topic:
http://www.colorado.edu/physics/EducationIssues/ModernPhysics/Lecture_Notes/CSMSP11_Lecture11_AtomicSpectra(asgiven).pdfWhen energy is released in an atom, such as when an electron falls from a higher energy state to a lower energy state, it will emit a photon - that is the same as saying it will emit EM wave. That released EM wave (photon) contains the energy it released.
Mass and energy are the same thing. Photon (mass-less) carries momentum.
Photon and EM wave relationship is a different concept from wave-particle duality.
Wave-particle duality is the concept that all particles exhibits wave properties and the reverse is also true. You can pick any subatomic particle, be it photon, electron, alpha particle, or for that matter, any particle. When you treat it as a particle, you can measure it's particle properties. When you treat it as a wave, you can measure its wave properties. You will find alpha particles doing crazy things like being at two places at the same time when you are treating it as a wave.
Back to photon - current theory is, all EM waves travel at c. However, there are studies pointing to possibly not all photons travel at c. U.C. Davis study on how gamma ray appears to be slower is pointing at possibly not all photons travel at c.
https://www.ucdavis.edu/news/gamma-ray-delay-may-be-sign-new-physics/A lot of work are being done. We don't know all there is to know yet.