I had the same question. When I researched this at @Electricity is energy [the real title of the article is “Electricity Is NOT Energy”], I found out that electrons are tiny particles of matter. They are the bits of matter within an atom that vibrate around the nucleus of an atom. Electrons can also fly about freely or travel slowly and are not just found within atoms. In a copper wire, for example, they can be found loose, outside atoms, traveling slowly, a few inches per minute. 

Electrons have a negative charge, which means only that they move away from other negatively charged matter (other electrons) and are drawn to positively charged matter (protons, often ones in the nuclei of atoms). 

But photons are units (packets of energy) of an electromagnetic wave. They are not bits of matter. A type of photon that we experience very intimately all the time is the photons of visible light. These hit our retina and cause chemical changes or hit a photographic plate. In both cases, the photons create chemical changes which ultimately create images. 

Light is just one type of electromagnetic energy. Other types of electromagnetic energy are X-rays (a high-energy wave), waves that carry radio signals and TV signals, microwaves in a microwave oven, etc. All of the bits of energy that are associated with these waves are photons. 

Photons have neither negative nor positive charge. They are not matter and have no mass. They travel the speed of light when in a vacuum like in outer space (which is not a complete vacuum, really). But they can travel much slower when traveling through a medium like water or even air. 

Photons and electrons interact to create flows of electricity. Both are involved. Electricity is not merely a flow of electrons in a wire; it is also a flow of photons in an electromagnetic wave.