The key differences here are where the inhibitor binds to the enzyme, competitive bind to the active site and as such compete directly with the normal substrate of the enzyme. Noncompetitive bind to a site other than the active site (sometimes known as the allosteric site) and change the structure and thus binding capability of the active site. Because of this key difference competitive inhibitors show reversibility if you add more of the enzymes normal substrate whereas noncompetitive inhibitors do not.