Non-hydraulic lime (CL or DL 70-90) is sold as either hydrated lime or putty lime; they set and harden through drying out and absorbing carbon dioxide from the air. This means they have a very slow set: CO2 is only absorbed when certain conditions are met. They are the softest, most breathable limes available. These limes are also known as fat-lime, calcium-lime or air-lime.
Hydrated lime simply means that a controlled amount of water is added to quicklime to make a powder that is more stable and safe to handle. This can be done to hydraulic lime or non-hydraulic lime.