Define 'not move at all'.
In relation to what?
Period.
"Geocentric" means the idea that the earth is fixed in it's place, perhaps by God, and does not move at all.
The rest of the universe moves around this stationary earth.
"Heliocentric" is the idea that due to the laws of gravity, the largest mass in a system like the solar system is the center of that system.
From Wikipedia: Modern Geocentrism
Modern geocentrism is a belief currently held by certain groups that the Earth is the center of the universe and does not move. The prime motivating factor for the modern belief, as opposed to the geocentrism of Ptolemy, is explicitly religious. Advocates generally argue that literal interpretations of certain Biblical passages demand that the Earth be properly described as being the center of the universe. Alternatively, in the case of Catholic geocentrists, scripture authoritatively interpreted by statements of Church Fathers and various Popes is used to justify their belief, even though this viewpoint is no longer endorsed by the Church itself.