The inhibitor has a similar shape to the usual substrate for the enzyme, and competes with it for the active site. However, once it is attached to the active site, nothing happens to it. It doesn't react - essentially, it just gets in the way.
basically they are competing against the enzyme substrate molecules for the active site, if the competitive enzyme combines with active site of the enzyme, this means that there is a limited number of active site of the enzyme available for the enzyme substrate molecules. this subsequently decreases the enzyme activity.
A non-competitive inhibitor does not attach itself to the active site, but attaches on the allosteric site of the enzyme. By attaching there it changes the shape of the active site, so that i is not complementary to the enzyme substrate.Because there isn't any competition involved between the inhibitor and the substrate, increasing the substrate concentration won't help.
so the difference would be the following:-
the competitive inhibitor competes against the enzyme subtrate for the active site whereas the non-competitive inhibitor does
the competitive inhibitor attaches to the active site whereas the non-competitive inhibitor binds to the alloseric site.
hope that helped