The different types of inhibition include competitive, non-competitive, uncompetitive, and feedback inhibition. Competitive inhibition blocks enzyme activity by occupying the active site, while non-competitive inhibition alters enzyme function without blocking the active site. Uncompetitive inhibition binds to the enzyme-substrate complex, and feedback inhibition regulates pathways by the end product suppressing enzyme activity upstream. Each type modulates metabolic pathways by altering enzyme efficacy and regulating metabolic flux.