When considering fertilizers, it's important to note that the vast majority are produced using non-organic compounds. The basic formula seen in fertilizers preparation (10-10-10, for example) refer to the three primary nutrients for plants: nitrogen, phosphorus, and potassium. These are certainly naturally occuring mineral elements, but they're not organically derived. In fact, they're typically derived from natural gas (nitrogen) or from mining (phosphorus and potassium).
In contrast, the nutrients in organic fertilizers are derived from natural, organic compounds such as compost, manure, and worm castings. As far as your plants are concerned, organic and inorganic nutrients are relatively the same. Depending on the formulation, both types of fertilizer can supply essentially identical nutrient levels. Many organic fertilizers also incorporate symbiotic fungi and bacteria to break the organic nutrients down so they're readily available.