The term "imine" was coined in 1883 by the German chemist Albert Ladenburg.
Usually imines refer to compounds with the general formula RC=NR, as discussed below. In the older literature, imine refers to the aza-analogue of an epoxide. Thus, ethylenimine is the three-membered ring species aziridine CHNH. The relationship of imines to amines having double and single bonds can be correlated with imides and amides, as in succinimide vs  acetamide. 
Imines are related to ketones and aldehydes by replacement of the oxygen with an NR group.  When R = H, the compound is a primary imine, when R is hydrocarbyl, the compound is a secondary imine.  If this group is not a hydrogen atom, then the compound can sometimes be referred to as a Schiff base.  When R is OH, the imine is called an oxime, and when R is NH the imine is called a hydrazone.
A primary imine in which C is attached to both a hydrocarbyl and a H is called a primary aldimine; a secondary imine with such groups is called a secondary aldimine. A primary imine in which C is attached to two hydrocarbyls is called a primary ketimine; a secondary imine with such groups is called a secondary ketimine.
N-Sulfinyl imines are a special class of imines having a sulfinyl group attached to the nitrogen atom.