Are there any differences between quasars and Active Galactic Nuclei (AGN)? As I understand it, they are both caused by extremely luminous electromagnetic emission from material accreting onto a super-massive black hole. If they have the same source, is there still some fundamental difference between them (and if so what is it) or are they two names for the same thing?
All quasars are AGN, but not all AGN are quasars.
AGN is a terminology that comes later than quasars. Quasars is the term applied at the beginning, when the first objects of this type have been discovered. They were radio-loud and point-like (the so-called quasi-stellar radio sources). This characterization still holds nowadays. Another property is that quasars are cosmological, that is they are objects in the distant universe (redshift $z > 1$).
AGN is the most general term we can use to refer to active galaxies. AGN include all of them (Seyfert galaxies, Quasars, Blazars, etc.). In the end, it seems that the difference among various types of AGN is due to a mix of angle-of-sight/epoch-of-observation.
A quasar is a type of AGN. Its main property is that it's galaxy axis points towards the earth and this way we receive its light and radio signals. That's why they are one of the most energetic AGN. Here you can see a relation of all the AGN types: http://en.wikipedia.org/wiki/Active_galactic_nucleus#Summary