First, let's define "fertilizer". Fertilizers are chemicals or materials which contain nutrients necessary for healthy plant/grass growth. These materials may be from a natural source or a man-made source. Nitrogen (N), phosphorus (P) and potassium (K) are the major nutrients necessary for the growth and development of all plants, including grasses. You see these elements listed on the fertilizer bag and always in that same order.
Organic fertilizer is derived from a natural source (e.g., manure, urea). It tends to be slow to break down and supply the plant with its nutrients.
Synthetic fertilizer is man-made. It may be organic (such as urea) or it may be a more complicated chemical formulation.
Soluble is a term that means that the fertilizer can break down or be released with the availability of water. For fertilizer, water soluble nitrogen (WSN) is nitrogen that is readily available to plants and can be immediately absorbed by the plant. Urea and ammonium are the most common fertilizer components. Use of soluble fertilizers causes immediate growth. A Spring lawn fertilizer typically has a high ratio of water soluble nitrogen.
Insoluble means that the fertilizer is not readily available to the plant. With water insoluble nitrogen (WIN), the nitrogen is not readily available to the plants. The nitrogen is released slowly for weeks during the growing season. Specialty fertilizers are more apt to contain some of the nitrogen component as water insoluble nitrogen.