These words refer to putting some control on action, movement, development, or progress, but they differ in minor ways. Check means "to arrest suddenly," "to halt": "The rider checked his horse and leaped from the saddle." Curb implies the use of a chain, strap, rope, or similar device for guiding, controlling, or forcing within boundaries: "The rider used a heavy bridle to curb his mount." Restrain suggests the use of actual force to hold back or control: "The referee restrained the angry player by grasping his arms." Constrain is related to restrain but also implies the idea of compulsion: "His conscience constrained him to return the money." In ordinary conversation, however, one may curb or check his tongue, and one may check, curb, restrain, or even constrain his impulses and desires.
Dictionary of problem words and expressions. Harry Shaw. 1975.