Grignard reactions and reagents were discovered by and are named after the French chemist François Auguste Victor Grignard (University of Nancy, France), who described them in 1900. He was awarded the 1912 Nobel Prize in Chemistry for this work. 
The reaction of an organic halide with magnesium is not a Grignard reaction, but provides a Grignard reagent. 
Classically, the Grignard reaction refers to the reaction between a ketone or aldehyde group with a Grignard reagent to form a primary or tertiary alcohol. However, some chemists understand the definition to mean all reactions of any electrophiles with Grignard reagents. Therefore, there is some dispute about the modern definition of the Grignard reaction. In the Merck Index, published online by the Royal Society of Chemistry, the classical definition is acknowledged, followed by "A more modern interpretation extends the scope of the reaction to include the addition of Grignard reagents to a wide variety of electrophilic substrates." This variety of definitions illustrates that there is some dispute within the chemistry community about the definition of a Grignard reaction. 
Shown below are some reactions involving Grignard reagents, but they themselves are not classically understood as Grignard reactions.