The key thing here is, if my Biology memory serves me well, is that competitive inhibition is where the inhibitor competes with the substrate by attaching to the enzyme via the active site.
So this would regulate the rate of reaction for whatever the context is, as enzyme activity is proportional to the rate of reaction. If some enzymes are "blocked" with the inhibitor, this lessens the rate of reaction.
Non-competitive inhibitors instead bind to the allosteric site of an enzyme, which often, denatures the enzyme and consequently usually destroys it. So in a non-competitive inhibitor, the concentration of the substrate has no effect because the active sites of the enzyme become warped - so no amount of substrate can bind to the active site.