Hydraulic lime is a variety of slaked lime used to make lime mortar. Hydraulicity is the ability of lime to set under water. Hydraulic lime is produced by heating calcining limestone that contains clay and other impurities. Calcium reacts in the kiln with the clay minerals to produce silicates that enable the lime to set without exposure to air. Any unreacted calcium is slaked to calcium hydroxide. Hydraulic lime is used for providing a faster initial set than ordinary lime in more extreme conditions (including under water).
Garden Lime is coarse ground Limestone, which is Calcium Carbonate (CaCO2), with small percentages of Magnesium Carbonate and Magnesium Oxides.
Calcium hydroxide, traditionally called slaked lime, hydrated lime, slack lime, or pickling lime, is a chemical compound with the chemical formula Ca(OH)2. It is a colourless crystal or white powder, and is obtained when calcium oxide (called lime or quicklime) is mixed, or "slaked" with water. It can also be precipitated by mixing an aqueous solution of calcium chloride and an aqueous solution of sodium hydroxide. The name of the natural, mineral form is portlandite. It is a relatively rare mineral, known from some volcanic, plutonic, and metamorphic rocks. It has also been known to arise in burning coal dumps.
SO in short, there three different substances. The point of garden lime is to add alkalinity to the soil. Hydraulic Lime is not going to behave the same in the soil as garden lime since its chemistry is different,. and i woudl suggest the process it goes through will make it less reactive and less predictable in respect of what it will do in the soil, and whats more, its got stuff in you might not want in your plants, like silicon. Personally, i wouldnt bung it on my plot.