What is the difference between the geocentric and heliocentric models?
One way to remember the difference between the geocentric model and the heliocentric model is to look at the etymology of the words.
Geocentric means the Earth is at the center. The prefix geo means of the Earth. Thus geometry is the measure of the earth, geology is the study of the earth, etc...
Heliocentric means the sun is at the center. The prefix helio means of the sun. One can speak of the heliosphere, the region of space dominated by the sun gravitationally or the heliopause which is the theoretical edge where the stellar wind is stopped by the interstellar medium.
The geocentric model posited that the entire universe revolved about Earth. After Aristotle this theory is most attached to Ptolemy who wrote the Algamest. In the Algamest Ptolemy collected and refined the theories for planetary motions including the use of epicycles to describe the orbits. This system was widely held in the West until the sixteenth century when a predictive geocentric model was proposed.
The heliocentric model puts the sun at the center of the solar system. This theory was put forth in pre-Socratic time, but was not widely believed and disappeared possibly due to the loss of ancient greek works. Copernicus published one of the first descriptions of the theory with work by Kepler, Galileo, and Newton providing mathematical support later.