They have the similar stem крест (cross) so in a manner they have some common origins. Still, a Christian would be христианин.Originally Posted by ingberlin
Крест - means a cross on a church. Окрестность - the surroundings originates from this word (an area that surrounds the church). Peasants (крестьяне) were serfs in Russia so they were bound to the land - usually a village with a church in the center (around the cross).
The word христианин, from the other hand, comes from the name of Jesus (Христос in Russian). The two words sound alike but the only similarity comes from the link between Christ and the cross.