These words mean "at or within a short distance or interval in time or space," but close is closer or nearer than near. That is, use close when you wish to stress immediate proximity: "a close shave," "a close call," "a close friend." Near more often conveys the idea of a narrow margin or approximation: "a near resemblance," "a near escape," "near neighbors." A photo finish is a close race, not a near one. Also, one does not set a near-record. Only a record is recorded, not a near-record.
Dictionary of problem words and expressions. Harry Shaw. 1975.