From Wiki answers:
Shock Absorber & Strut
To answer this let me start with the basic components of a suspension.
The suspension spring absorbs energy and reduces vertical acceleration of wheel.
The damper stops the motion of the mass-spring system which would otherwise keep oscillating.
A bump stopper or jounce bumper or... there are hundred other names to this rubber / PU piece, prevents metal-to-metal contact and thereby the 'clang' produced when spring becomes solid.
A ball joint is a spherical headed screw. The head is inserted into a dome and the screw can articulate in a conical envelope when the dome is fixed.
A control arm or wishbone is schematically a triangular suspension link where one vertex is a ball joint (upper or lower) and the opposite side is a hinge joint. These link controls the wheel path when it articulates. There is usually an upper control arm and a lower control arm.
A shock absorber or coil-over-shox is a unit in which spring & bump stopper are arranged concentric (rather coaxial) with the damper to save space required for seperate installation of each.
A strut is a coil-over-shox with additional degrees of freedom for steering the wheel (provided by a bearing which partially replaces a ball joint) and articulation of the wheel (provided by the top mount which doubles in as the upper wishbone / control arm).
A strut is thus, a combination of a number of suspension components viz. spring, damper, bump stopper, upper control arm and probably one ball joint.
A strut and a coil-over-shox are not interchangable. If you put a simple coil-over-shox in place of strut, you won't be able to steer the vehicle and if you do otherwise, the directional stability will be lost. A strut is usually used in front suspension and a coil-over-shox is generally a part of rear suspension.