What is the difference between Registers, Grilles and Diffusers?

>>>diifusers for supply and return air (square or jet or linear diffuser )

must be installed with a neck

fixed control air direction

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>>>grills for supply and return air (return bar grills or side wall grill )

must be installed with a neck or direct on the duct

fixed control air direction in return bar grills

manual control air direction in side grill 

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>>>register = grill + damper

must be installed with a neck or direct on the duct

fixed control air direction in return bar grills

manual control air direction in side grill 

Diffuses can be with control or without control and have variety of shapes and applications.

Grilles is without damper and register is with damper to control air movement\\flow

check the link below it describes exactly what u asked for :

http://www.achrnews.com/events/-proper-selection-of-grilles-registers-and-diffusers

Grille: A fixed opening through which air passes. Typically used for return air applications.

Register: A grille equipped with a damper which supplies conditioned air. Typically used for supply air applications.

Diffuser: An air flow device designed to discharge conditioned air in a specific direction, path, or pattern. Used for supply air applications

GRD – Grilles, Registers, and Diffusers