The terms, lone pair and bonding pair, are used in Valence bond theory, which is used to describe chemical bond formations using the overlap of electrons. A lone pair consists of 2 electrons, in the same orbital from the same atom, which are not involved in bonding. On the other hand, a bonding pair is 2 electrons, from different atoms, which overlap to form a pi or sigma bond. In other words, a lone pair is a non-bonding pair.
Both lone pairs and bonding pairs determine the shape of the molecule, but in general, there is stronger repulsion between lone pairs and other bonding pairs than bonding pairs and other bonding pairs.