The basic ingredients of both fertilizers are about the same. Organic fertilizers are the result of the natural decomposition of plant and animal waste. Inorganic fertilizers are mined or manufactured. The contents of both types are basically the same except for the source. Chemical fertilizers are generally derived from non-renewable resources.
Chemical fertilizers generally are produced in a form a plant can use immediately. Chemical fertilizers are generally easier to apply and can be applied more accurately in specific amounts. Organic fertilizers are not in a form that plants can use right away. Organics require time for the fertilizer to break down in the soil and convert to a fertilizer the plant can use. Another difference is that inorganic materials last a lot longer in the soil and would leach or wash over a much longer period of time verses inorganic materials.