There is a lot more that could be written on this topic, but here are the quick and dirty differences between calcium sources for your soil.
Agricultural Lime: Calcium carbonate – CaC03 Pure calcium carbonate is used to help prevent the spread of various diseases, such as powdery mildew, black spot, and blossom end rot. Other benefits of calcium include, protection from heat stress, increases metabolic functions in plant cells, leading to a greater intake of other nutrients such as nitrogen and phosphorus. Additionally it helps to increase general cell wall structure. Adding Ag. Lime to your soil will also raise your PH making it more alkaline.
Dolomite: Dolomitic Lime contains calcium carbonate, bringing benefits similar to Ag Lime, while also providing magnesium which is important for plants’ utilization of nitrogen, phosphorus and sulfur. Having an excess of magnesium in your soil can cause a break down in soil structure, resulting in hard compact soils.
Gypsum: Calcium sulfate, or Sulfate of Lime – CaS042H20, due to its sulfur content Gypsum does not raise the soil PH like lime, and there is some debate as to whether it lowers soil PH. Gypsum helps liberate potash for plant use. Gypsum can also help break up compact and clay filled soils by correcting excess amounts of magnesium in your soil.
Oyster Shell Flour: in addition to a large percentage of calcium carbonate, Oyster shell flour contains about 1-% phosphoric acid, which makes oyster shell flour a source of both lime (calcium) and phosphorus. Oyster shell will also slightly raise your soils PH over time. Variable particle size provides both immediate and long-term, slow release, fertilization.